#### W Steven Gray

231K KAUFMAN HALL

NORFOLK, 23529

W. Steven Gray received the B.S. degree in electrical engineering from Purdue University, West Lafayette, IN, in 1983, the M.S. degree in electrical engineering, the M.S. degree in applied mathematics, and the Ph.D. in electrical engineering from the Georgia Institute of Technology, Atlanta, in 1985, 1988, and 1989, respectively. He is currently with the Electrical and Computer Engineering Faculty, Old Dominion University, Norfolk, VA. His research interests include modeling and control theory for nonlinear systems.

**Ph.D.** in Electrical Engineering, Georgia Institute of Technology, (1989)

**M.S.** in Applied Mathematics, Georgia Institute of Technology, (1988)

**M.S.** in Electrical Engineering, Georgia Institute of Technology, (1985)

**B.S.** in Electrical Engineering, Purdue University, (1983)

## Contracts, Grants and Sponsored Research

- Gray, W. S. and Gonzalez, O. "Design and Analysis of Recoverable Flight Control Systems for Harsh Environments via the SPIDER Architecture" $1,251,841. Federal. 2007 - 2012
- Gray, W. S. and Gonzalez, O. "Advanced Concepts for Recoverable Controllers in Safety Critical Systems" $402,562. Federal. 2004 - 2007
- Gray, W. S. and Gonzalez, O. "System Level Effects of Neutron Induced Single Event Upsets on Recoverable Digital Control Systems" $400,000. Federal. 2003 - 2006
- Gray, W. S. and Gonzalez, O. "Performance Analysis and Validation of High Efficiency Error Recovery Algorithms for Safety Critical Systems" $518,864. Federal. -
- Gray, W. S. and Gonzalez, O. "Hybrid Modeling and Analysis of Error Recovery in Safety Critical Flight Control Systems" $119,996. Federal. 2002 - 2005
- Gray, W. S. and Gonzalez, O. "Supplement to ODURF Project #101831" $17,191. Federal. 2002 - 2003
- Gray, W. S. and Gonzalez, O. "Stochastic Dynamical Models for Digital Control Systems in Electromagnetic Environments " $524,000. Federal. 2000 - 2003
- Gray, W. S. and Zahorian, S. "Analytical Synthesis of Sensory Neural Networks for Computer Vision" $390,000. Federal. -
- Gray, W. S., Gupta, M. and Gonzalez, O. "Center for Photon Engineering of Materials and Systems" $600,000. Federal. -
- Gray, W. S. and Gonzalez, O. "Robust Stability and Performance of a Closed-Loop Computer Control System Subject to Electromagnetic Disturbances" $177,000. Federal. 1999 - 2000
- Gray, W. S., Britcher, C. P. and Gonzalez, O. "Supplemental Funds for Characterization, Control and Commissioning of the Magnetic Suspension and Balance System for the Princeton/ONR High Reynolds Number Testing Facility" $40,000. Other. 1999 - 2000
- Gray, W. S., Britcher, C. P. and Gonzalez, O. "Characterization, Control and Commissioning of the Magnetic Suspension and Balance System for the Princeton/ONR High Reynolds Number Testing Facility" $100,000. Other. 1998 - 2000
- Gray, W. S. and Scherpen, J. "Balancing and Model Reduction for Nonlinear Dynamical Systems" $9,000. Other. -
- Gray, W. S. "Model Reduction for Nonlinear Systems Via Balanced Realizations" $240,000. Federal. -
- Gray, W. S., Scherpen, J. and Mesko, J. "Balancing and Model Reduction for Nonlinear Dynamical Systems" $6,000. Other. 1997 - 1999
- Gray, W. S. and Gonzalez, O. "Stability Analysis and Augmentation of a Closed-Loop Computer Control System Subject to Electromagnetic Disturbances" $175,000. Federal. 1997 - 1998
- Gray, W. S. "A Modern Curriculum on the Control of Non-linear Dynamical Systems" $6,000. Federal. -
- Gray, W. S. "Nonlinear Control Methodologies for Aerospace Applications" $50,000. Federal. -
- Gray, W. S., Nabet, B., Pinter, R. and Tonkin, S. "Sensory Visual Motion Detection and Visual Motion Detection Sensors" $333,000. Federal. -
- Gray, W. S. "Neural Control of Magnetic Suspension Systems for Aerospace Applications" $100,000. Federal. 1993 - 1994
- Gray, W. S. "Feedback Linearizing Controllers for Stochastic Systems with Nonaffine Controls" $138,000. Federal. -
- Gray, W. S. and Kam, M. "Distributed Detection and Sensor Fusion" $161,000. Other. -
- Gray, W. S. "Engineering Issues in Designing Feedback Linearizing Controllers" $3,500. Other. 1991 - 1991
- Gray, W. S. "Engineering Issues in Designing Feedback Linearizing Controllers" $70,000. Federal. -
- Gray, W. S. and Nagvajara, P. "Infrastructure for Research in Microelectronics, Real-Time Systems and Signal Processing" $931,000. Federal. -
- Gray, W. S. "Realization Theory and Numerical Issues for Singular Systems" $5,000. Other. -
- Gray, W. S. "Realization Theory and Numerical Issues for Singular Systems" $70,000. Federal. -
- Gray, W. S. "Realization Theory and Numerical Issues for Singular Systems" $20,000. Federal. -

## Research Interests

Research Interests: Formal power series methods for nonlinear systems analysis; realization theory and modelreduction for nonlinear systems; fault-tolerant control for safety critical systems.

## Articles

- Chavez Fuentes, J. R., Gonzalez, O. and Gray, W. S. (2018). Stability, performance and sensitivity analysis of I.I.D. Jump linear systems.
*International Journal of Control*91 (6) , pp. 1460-1472. - Gray, W., Duffaut Espinosa, L. A.. and Ebrahimi-Fard, K. (2017). Discrete-time approximations of Fliess operators.
*Numerische Mathematik*137 (1) , pp. 35--62. - Thitsa, M. and Gray, W. S. (2012). On the Radius of Convergence of Interconnected Analytic Nonlinear Systems.
*SIAM Journal on Control and Optimization*50 (5) , pp. 2786-2813. - Gray, W. S., Herencia-Zapana, H., Duffaut Espinosa, L. and Gonzalez, O. (2009). Bilinear System Interconnections and Generating Series of Weighted Petri Nets.
*Systems and Control Letters*58 (12) , pp. 841-848. - Tejada, A., Gonzalez, O. and Gray, W. S. (2008). Stability of Digital Control Systems Implemented in Error-Recoverable Computers.
*International Journal of Control*81 (11) , pp. 1665-1681. - Zhang, H., Gray, W. S., Gonzalez, O. and Lakdawala, V. K. (2008). Output Tracking Performance of a Recoverable Digital Flight Control System in Neutron Environments.
*IEEE Transactions on Aerospace and Electronic Systems*44 (4). - Gray, W. S. and Wang, Y. (2008). Noncausal Fliess Operators and Their Shuffle Algebra.
*International Journal of Control special issue for the occasion of M. Fliess’s 60th birthday)*81 (3) , pp. 344-357. - Gray, W. S., Zhang, H. and Gonzalez, O. (2008). Performance Analysis of Digital Flight Control Systems with Rollback Error Recovery Subject to Simulated Neutron-Induced Upsets.
*IEEE Transactions on Control Systems Technology*16 (1) , pp. 46-59. - Li, Y. and Gray, W. S. (2006). The Formal Laplace-Borel Transform of Fliess Operators and the Composition Product.
*International Journal of Mathematics and Mathematical Sciences*2006 (Article ID 34217) , pp. 1-14. - Gray, W. S. and Verriest, E. (2006). Balanced Realizations Near Stable Invariant Manifolds.
*Automatica*42 (4) , pp. 653-659. - Gray, W. S. and Li, Y. (2005). Generating Series for Interconnected Analytic Nonlinear Systems.
*SIAM Journal on Control and Optimization*44 (2) , pp. 646-672. - Gray, W. S. and Scherpen, J. (2005). Hankel Singular Value Functions from Schmidt Pairs for Nonlinear Input-Output Systems.
*Systems and Control Letters*54 (2) , pp. 135-144. - Gray, W. S. (2004). Book Review: Nonlinear System Identification – Input-Output Modeling Approach, Volumes 1&2 by R. Haber and L. Keviczky.
*Automatica*, pp. 901-903. - Gonzalez, O., Gray, W. S. and Tejada, A. (2002). Analytical Tools for the Design and Verification of Safety Critical Control Systems.
*2001 SAE Transactions - Journal of Aerospace*110 (1) , pp. 481-490. - Scherpen, J. and Gray, W. S. (2002). Nonlinear Hilbert Adjoints: Properties and Applications to Hankel Singular Value Analysis.
*Nonlinear Analysis: Theory, Methods & Applications*51 (5) , pp. 883-901. - Fujimoto, K., Scherpen, J. and Gray, W. S. (2002). Hamiltonian Realizations of Nonlinear Adjoint Operators.
*Automatica*38 (10) , pp. 1769-1775. - Gray, W. S. and Wang, Y. (2002). Fliess Operators on Lp Spaces: Convergences and Continuity.
*Systems and Control Letters*46 (2) , pp. 67-74. - Gray, W. S. and Scherpen, J. (2001). On the Nonuniqueness of Singular Value Functions and Balanced Nonlinear Realizations.
*Systems and Control Letters*44 (3) , pp. 219-232. - Scherpen, J. and Gray, W. S. (2000). Minimality and Local State Decompositions of a Nonlinear State Space Realization Using Energy Functions.
*IEEE Transactions on Automatic Control*45 (11) , pp. 2079-2086. - Gray, W. S., Gonzalez, O. and Dogan, M. (2000). Stability Analysis of Digital Linear Flight Controllers Subject to Electromagnetic Disturbances.
*IEEE Transactions on Aerospace and Electronic Systems*36 (4) , pp. 1204-1218. - Gray, W. S. and Mesko, J. (1999). Observability Functions for Linear and Nonlinear Systems.
*Systems and Control Letters*38 (2) , pp. 99-113. - Gray, W. S. and Nabet, B. (1999). Volterra Series Analysis and Synthesis of a Neural Network for Velocity Estimation.
*IEEE Transactions on Systems, Man, and Cybernetics*29 (Part B) (2) , pp. 190-197. - Verriest, E. and Gray, W. S. (1995). A Geometric Approach to the Minimum Sensitivity Design Problem.
*SIAM Journal on Control and Optimization*33 (3) , pp. 863-881. - Bezick, S. and Gray, W. S. (1995). Guidance of a Homing Missile Via Nonlinear Geometric Control Methods.
*AIAA Journal of Guidance, Control, and Dynamics*18 (3) , pp. 441-448. - Kam, M., Zhu, Q. and Gray, W. S. (1992). Optimal Data Fusion of Correlated Local Decisions in Multiple Sensor Detection Systems.
*IEEE Transactions on Aerospace and Electronic Systems*28 (3) , pp. 916-920. - Herath, J. and Gray, W. S. (1991). High-Performance DSP Architectures for Intelligence and Control Applications.
*IEEE Control Systems Magazine*11 (4) , pp. 49-55.

## Book Chapters

- Gray, W. S. (1990). "The Parametric Sensitivity of Bilinear Dynamical Systems" in Realization and Modelling in System Theory (pp. 369-378) Boston: Birkh¨auser Boston Inc.
- Gray, W. S. (1988). "Robust Design Problems: A Geometric Approach" in Linear Circuits, Systems and Signal Processing: Theory and Application (pp. 321-328) Amsterdam: Elsevier Science Publishers B.V.

## Conference Proceeding

- Gray, W. S., Diffaut Espinosa, L. A. and Kell, L. T. (2017). Data-driven siso predictive control using adaptive discrete-time fliess operator approximations Piscataway, NJ: 21st International Conference on System Theory, Control and Computing (ICSTCC).
- Duffaut Espinosa, L. A. and Gray, W. S. (2017). Integration of output tracking and trajectory generation via analytic left inversion Piscataway, NJ: 21st International Conference on System Theory, Control and Computing (ICSTCC).
- Thitsa, M. and Gray, W. S. (2012). On the radius of convergence of cascaded analytic nonlinear system Orlando, Florida: Proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011).
- Thitsa, M. and Gray, W. S. (2011). On the Radius of Convergence of Cascaded Analytic Nonlinear Systems Auburn, Alabama: Proceedings of the 43rd IEEE Southeastern Symposium of System Theory.
- Yates, A., Torres-Pomales, W., Malekpour, M., Gonzalez, O. and Gray, W. S. (2010). High-Intensity Radiated Field Fault-Injection Experiment for a Fault-Tolerant Distributed Communication System (pp. 4.E.3-1-15) Salt Lake City, UT: Proc. 2010 Digital Avionics Systems Conference.
- Duffaut Espinosa, L., Gray, W. S. and Gonzalez, O. (2010). On the Absolute Global Convergence of Fliess Operators Driven by L2-Itô Processes (pp. 280-285) Tyler, TX: Proc. 42nd IEEE Southeastern Symposium on System Theory.
- Duffaut-Espinosa, L., Gray, W. S. and Gonzalez, O. (2010). On the Local Convergence of Fliess Operators Driven by L2-Itô Processes Atlanta, GA: Proc. 49th IEEE Conference on Decision and Control.
- Gray, W. S. and Thitsa, M. (2010). On the Radius of Convergence of Self-excited Feedback Connected Analytic Nonlinear Systems
*Proc. 49th IEEE Conference on Decision and Control*Atlanta, Georgia: Proceedings of the 49th IEEE Conference on Decision and Control. - Chavez-Fuentes, J., Gray, W. S. and Gonzalez, O. (2010). Performance Analysis of Fault Tolerant Control Systems with I.I.D. Upsets (pp. 6197-6204) Baltimore, MD: Proc. 2010 American Control Conference.
- Gray, W. S., Wang, R., Gonzalez, O. and Chavez-Fuentes, J. (2010). Tracking Performance Analysis of a Distributed Recoverable Boeing 747 Flight Control System Subject to Digital Upsets (pp. 548-554) Baltimore, MD: Proc. 2010 American Control Conference.
- Duffaut Espinosa, L., Gray, W. S. and Gonzalez, O. (2009). On Fliess Operators Driven by L2-Itô Random Processes (pp. 7478-7484) Shanghai:.
- Chavez Fuentes, J., Gonzalez, O. and Gray, W. S. (2009). Transformations of Markov Processes in Fault Tolerant Interconnected Systems (pp. 227-232) Proc. 2009 American Control Conference.
- Gray, W. S., Wang, R. and Gonzalez, O. (2008). A Performance Model for a Distributed Flight Control System Subject to Random Upsets (pp. 918-923) San Antonio, Texas: IEEE Conference on Control Applications.
- Gray, W. S. and Wang, Y. (2008). Formal Fliess Operators with Applications to Feedback Interconnections Blacksburg, VA: 18th International Symposium on the Mathematical Theory of Networks and Systems.
- Tejada, A., Herencia, H., Gonzalez, O. and Gray, W. S. (2008). Mean Square Stability Analysis of Sampled-Data Supervisor Control Systems (pp. 37-42) San Antonio, Texas: IEEE Conference on Control Applications.
- Gray, W. S., Herencia, H., Duffuat, L. and Gonzalez, O. On Cascades of Bilinear Systems and Generating Series of Weighted Petri Nets 47th IEEE Conference on Decision and Control.
- Chavez, J., Gonzalez, O. and Gray, W. S. (2008). Towards a Metric for the Assessment of Safety Critical Control Systems (pp. Paper AIAA 2008-6804 ) Honolulu, HI: AIAA Guidance, Navigation and Control Conference.
- Chavez, J., Gonzalez, O. and Gray, W. S. (2008). Transformations of Markov Processes in Fault Tolerant Interconnected Systems San Antonio, Texas: IEEE Conference on Control Applications.
- Chavez, J., Gonzalez, O. and Gray, W. S. (2007). A Black-Scholes Approach to Satisfying the Demand in a Failure-Prone Manufacturing System (pp. 154-158) Macon, GA: 39th IEEE Southeastern Symposium on System Theory.
- Herencia, H., Gonzalez, O. and Gray, W. S. (2007). Dynamically Colored Petri Net Representation of Nonlinear Sampled-Data Systems with Embedded Recovery Algorithms (pp. 97-102) New Orleans, LA: 46th IEEE Conference on Decision and Control.
- Tejada, A., Herencia, H., Gonzalez, O. and Gray, W. S. (2007). Mean Square Stability Analysis of Hybrid Jump Linear Systems Using a Markov Kernel Approach (pp. 3482-3487) New York City, NY: American Control Conference.
- Duffaut, L., Gray, W. S. and Gonzalez, O. (2007). On the Bilinearity of Cascaded Bilinear Systems (pp. 5581-5587) New Orleans, LA: 46th IEEE Conference on Decision and Control.
- Duffaut, L., Gray, W. S. and Gonzalez, O. (2007). On the Rationality of the Composition Product: A Survey (pp. 238-243) Macon, GA: 39th IEEE Southeastern Symposium on System Theory.
- Tejada, A., Gonzalez, O. and Gray, W. S. (2007). Stability Analysis of Hybrid Jump Linear Systems with Markov Inputs (pp. 6280-6285) New Orleans, LA: 46th IEEE Conference on Decision and Control.
- Tejada, A., Gonzalez, O. and Gray, W. S. (2006). A Measure-Theoretic Proof of the Markov Property for Hybrid Systems with Markovian Inputs (pp. 328-332) Cookeville, TN: 38th IEEE Southeastern Symposium on System Theory.
- Gray, W. S. and Verriest, E. (2006). Algebraically Defined Gramians for Nonlinear Systems (pp. 3730-3735) San Diego, CA: 45th IEEE Conference on Decision and Control.
- Verriest, E. and Gray, W. S. (2006). Geometry and Topology of the State Space via Balancing (pp. 840-848) 17th International Symposium on the Mathematical Theory of Networks and Systems.
- Lakdawala, V. K., Zhang, H., Gonzalez, O. and Gray, W. S. (2006). Markovian Statistical Data Analysis of Single-Event Upsets Triggered by High Intensity Neutrons (pp. 349-353) Cookeville, TN: 38th IEEE Southeastern Symposium on System Theory.
- Gray, W. S. and Wang, Y. (2006). Noncausal Fliess Operators and Their Shuffle Algebra (pp. 2805-2813) 17th International Symposium on the Mathematical Theory of Networks and Systems.
- Tejada, A., Gonzalez, O. and Gray, W. S. (2006). On the Markov Property for Nonlinear Discrete-Time Systems with Markovian Inputs (pp. 899-904) Minneapolis, MN: American Control Conference.
- Herencia, H., Gonzalez, O. and Gray, W. S. (2006). Towards a Theory of Sampled-Data Piecewise-Deterministic Markov Processes (pp. 944-949) San Diego, CA: 45th IEEE Conference on Decision and Control.
- Tejada, A., Gonzalez, O. and Gray, W. S. (2005). Asymptotic and Mean Square Stability Conditions for Hybrid Jump Linear Systems with Performance Supervision (pp. 569-574) Portland, OR: American Control Conference.
- Gray, W. S. and Li, Y. (2005). Local Convergence of the Feedback Product via the Asymptotics of the Catalan Numbers (pp. 6140-6145) 44th IEEE Conference on Decision and Control and 2005 European Control Conference.
- Gray, W. S. and Li, Y. (2005). On Feedback Connections of Analytic Nonlinear Systems and Combinatorics on Words (pp. 429-434) Atlanta, GA: 36th IEEE Southeastern Symposium on System Theory.
- Zhang, H., Gray, W. S. and Gonzalez, O. (2005). Performance Analysis and Validation of a Recoverable Flight Control System in a Simulated Neutron Environment (pp. Paper 2005-6430) San Francisco, CA: AIAA Guidance, Navigation and Control Conference.
- Zhang, H., Gray, W. S. and Gonzalez, O. (2005). Performance Analysis of Recoverable Flight Control Systems Using Hybrid Dynamical Models (pp. 2787-2792) Portland, OR: American Control Conference.
- Verriest, E. and Gray, W. S. (2004). Balanced Nonlinear Realizations (pp. 1164-1169) 43rd IEEE Conference on Decision and Control.
- Gray, W. S. and Verriest, E. (2004). Balanced Realizations Near Stable Invariant Manifolds 16th International Symposium on the Mathematical Theory of Networks and Systems.
- Zhang, H., Gray, W. S. and Gonzalez, O. (2004). Markov Jump-Linear Performance Models for Recoverable Flight Control Computers (pp. 408-412) Atlanta, GA: 36th IEEE Southeastern Symposium on System Theory.
- Patikulkarni, S., Herencia, H., Gray, W. S. and Gonzalez, O. (2004). On the Stability of Jump-Linear Systems Driven by Finite-State Machines with Markovian Inputs (pp. 2534-2539) Boston, Massachusetts: American Control Conference.
- Gonzalez, O., Herencia, H. and Gray, W. S. (2004). Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller (pp. 4128-413) 43rd IEEE Conference on Decision and Control.
- Gray, W. S., Gonzalez, O. and Herencia, H. (2004). Stochastic Stability of Sampled Data Systems with a Jump Linear Controller (pp. 256-260) Atlanta, GA: 36th IEEE Southeastern Symposium on System Theory.
- Li, Y. and Gray, W. S. (2004). The Formal Laplace-Borel Transform, Fliess Operators and the Composition Product (pp. 333-337) Atlanta, GA: Proc. 36th IEEE Southeastern Symposium on System Theory.
- Tejada, A., Gonzalez, O. and Gray, W. S. (2004). Towards Stability Analysis of Jump Linear Systems with State-Dependent and Stochastic Switching (pp. 1893-1898) Boston, MA: American Control Conference.
- Gray, W. S., Zhang, H. and Gonzalez, O. (2003). Closed-Loop Performance Measures for Flight Controllers Subject to Neutron-Induced Upsets (pp. 2465-2470) Maui, Hawaii: 42nd Conference on Decision and Control.
- Eure, K., Belcastro, C., Gray, W. S. and Gonzalez, O. (2003). Neutron Particle Effects on a Quad-Redundant Flight Control Computer (pp. 1.B.2-1–8) Indianapolis, Indiana: Digital Avionics Systems Conference.
- Gray, W. S., Patikulkarni, S. and Gonzalez, O. (2003). Stochastic Stability of a Recoverable Computer Control System Modeled as a Finite-State Machine (pp. 2240-2245) Denver, Colorado: American Control Conference.
- Li, Y., Song, M. and Gray, W. S. (2003). A Self-adaptive Predictive Congestion Control Model for Extreme Networks (pp. 327-332) Proc. of the International Conference on Computer, Proc. of the International Conference on Computer, Proc. of the International Conference on Computer, Communication and Control Technologies.
- Gonzalez, O., Tejada, A. and Gray, W. S. (2002). Analysis of Design Tradeoffs in Rollback Recovery Methods for Fault Tolerant Digital Control Systems (pp. 4801-4806) Anchorage, Alaska: American Control Conference.
- Gray, W. S. and Li, Y. (2002). Fliess Operators in Cascade and Feedback Systems (pp. 173-178) Princeton, NJ: Conference on Information Sciences and Systems.
- Gray, W. S. and Li, Y. (2002). Generating Series for Nonlinear Cascade and Feedback Systems (pp. 2720-2725) Las Vegas, NV: 41st IEEE Conference on Decision and Control.
- Gray, W. S. and Scherpen, J. (2002). Hankel Singular Value Functions from Schmidt Pairs for Nonlinear Input-Output Systems (pp. 3540-3545) Anchorage, Alaska: American Control Conference.
- Gray, W. S. and Li, Y. (2002). Interconnected Systems of Fliess Operators South Bend, Indiana: 15th International Symposium on the Mathematical Theory of Networks and Systems.
- Gray, W. S., Patikulkarni, S. and Gonzalez, O. (2002). Towards Hybrid Models of Recoverable Computer Control Systems (pp. 13.C.2-1-9) Irvine, CA: Digital Avionics Systems Conference.
- Gonzalez, O., Gray, W. S. and Tejada, A. (2001). Analytical Tools for the Design and Verification of Safety Critical Control Systems Seattle, WA: International Conference on Lightning and Static Electricity.
- Gray, W. S. (2001). Computing Hilbert Adjoints of Fliess Operators (pp. 481-486) Baltimore, MD: Conference on Information Sciences and Systems,.
- Verriest, E. and Gray, W. S. (2001). Discrete-Time Nonlinear Balancing (pp. 515-520) 5th IFAC Nonlinear Control Systems Design Symposium.
- Gray, W. S. (2001). Nonlinear Adjoints of Fliess Operators (pp. 2625-2630) Orlando, FL: 40th IEEE Conference on Decision and Control.
- Verriest, E. and Gray, W. S. (2001). Nonlinear Balanced Realizations (pp. 3250-3251) Orlando, FL: 40th IEEE Conference on Decision and Control.
- Gray, W. S. and Scherpen, J. (2001). Nonlinear Hilbert Adjoints: Properties and Applications to Hankel Singular Value Analysis (pp. 3582-3587) Arlington, VA: American Control Conference.
- Gonzalez, O., Gray, W. S., Tejada, A. and Patikulkarni, S. (2001). Stability Analysis of Electromagnetic Interference Upset Recovery Methods (pp. 4134-4139) Orlando, FL: IEEE Conference on Decision and Control.
- Gonzalez, O., Gray, W. S., Tejada, A. and Patikulkarni, S. (2001). Stability Analysis of Upset Recovery Methods for Electromagnetic Interference (pp. 1.C.4-1–9) Daytona Beach, FL: 2001 Digital Avionics Systems Conference.
- Gonzalez, O., Gray, W. S. and Patilkulkarni, S. (2000). Analysis of Memory Bit Errors Induced by Electromagnetic Interference in Closed-Loop Digital Flight Control Systems (pp. 3.C.5-1-9) Philadelphia, PA: Digital Avionics Systems Conference.
- Britcher, C., Gonzalez, O., Gray, W. S., Gomeiz, O., Barkley, J. and Jafri, A. (2000). Design of a Magnetic Suspension and Balance System for the Princeton/ONR High Reynolds Number Testing Facility (pp. 675-683) Santa Barbara, CA: 5th International Symposium on Magnetic Suspension Technology.
- Gray, W. S. and Wang, Y. (2000). Fliess Operators on Lp Spaces: Convergence and Continuity (pp. 4385-4390) 39th IEEE Conference on Decision and Control.
- Verriest, E. and Gray, W. S. (2000). Flow Balancing Nonlinear Systems 14th International Symposium on Mathematical Theory of Networks and Systems.
- Scherpen, J., Fujimoto, K. and Gray, W. S. (2000). Hamiltonian Extensions, Hilbert Adjoints and Singular Value Functions for Nonlinear Systems (pp. 5102-5107) 39th IEEE Conference on Decision and Control.
- Fujimoto, K., Scherpen, J. and Gray, W. S. (2000). Hamiltonian Realizations of Nonlinear Adjoint Operators (pp. 39-44) Princeton, NJ: Lagrangian and Hamiltonian Methods for Nonlinear Control, (IFAC Workshop).
- Scherpen, J., Fujimoto, K. and Gray, W. S. (2000). On Adjoints and Singular Value Functions for Nonlinear Systems (pp. FP8-7-12) Princeton, NJ: Conference on Information Sciences and Systems.
- Gray, W. S. and Wang, Y. (2000). Properties of Fliess Operators on Lp-Spaces (pp. FP8-1-6) Princeton, NJ: Conference on Information Sciences and Systems.
- Gray, W. S., Gonzalez, O. and Patikulkarni, S. (2000). Stability of Digital Control Systems Subject to Jump Linear Random Perturbations (pp. 1154-1159) 39th IEEE Conference on Decision and Control.
- Scherpen, J. and Gray, W. S. (2000). State Dependent Matrices and Balanced Energy Functions for Nonlinear Systems 14th International Symposium on Mathematical Theory of Network and Systems.
- Gray, W. S. and Verriest, E. (1999). Balancing Nonlinear Systems Near Attracting Invariant Manifolds European Control Conference.
- Gray, W. S., Gonzalez, O. and Dogan, M. (1999). Digital Linear State Feedback Control Subject to Electromagnetic Disturbances (pp. 3500-3504) San Diego. CA: American Control Conference.
- Scherpen, J. and Gray, W. S. (1999). Hankel Structure for Nonlinear Input-Output Systems and State-Space Realizations (pp. 331-363) First Nonlinear Control Network Pedagogical School.
- Gray, W. S. and Nabet, B. (1999). Modeling the Nonlinear Mapping in a Neural Based Motion Detector (pp. 245-252) Second International Conference on Nonlinear Problems in Aviation and Aerospace.
- Scherpen, J. and Gray, W. S. (1999). On Singular Value Functions and Hankel Operators for Nonlinear Systems (pp. 2360-2364) San Diego, CA: American Control Conference.
- Gray, W. S. and Scherpen, J. (1999). On the Nonuniqueness of Balanced Nonlinear Realizations (pp. 4736-4741) Phoenix, AZ: 38th IEEE Conference on Decision and Control.
- Gray, W. S. and Scherpen, J. (1999). On the Nonuniqueness of Singular Value Functions in Balanced Nonlinear Realizations (pp. 729-734) Baltimore, MD: Conference on Information Sciences and Systems.
- Gray, W. S., Gonzalez, O. and Dogan, M. (1999). Stochastic Perturbation Analysis of Computer Control Systems Subject to Electromagnetic Disturbances (pp. 1797-1802) Kohala Coast-Island, Hawaii: Conference on Control Applications.
- Gray, W. S., Gonzalez, O. and Dogan, M. (1999). Stochastic Perturbation Models of Electromagnetic Disturbances in Closed-Loop Computer Controlled Flight Systems (pp. 10.C.4-1-8) St. Louis, MO: Digital Avionics Systems Conference.
- Gray, W. S. and Gonzalez, O. (1998). EMI Models for Controller Analysis and Synthesis Seattle, WA: Digital Avionics Systems Conference.
- Gray, W. S. and Mesko, J. (1998). Energy Functions and Algebraic Gramians for Bilinear Systems (pp. 103-108) Preprints of the 4th IFAC Nonlinear Control Systems Design Symposium.
- Gray, W. S. and Scherpen, J. (1998). Hankel Operators and Gramians for Nonlinear Systems (pp. 1416-1421) Tampa, FL: 37th IEEE Conference on Decision and Control.
- Gray, W. S. and Gonzalez, O. (1998). Modeling Electromagnetic Disturbances in Closed-Loop Computer Controlled Flight Systems (pp. 359-364) Philadelphia, PA: American Control Conference.
- Scherpen, J. and Gray, W. S. (1998). Sufficient Conditions for Minimality of a Nonlinear Realization via Controllability and Observability Functions (pp. 3349-3353) Philadelphia, PA: American Control Conference.
- Verriest, E. and Gray, W. S. (1997). A Stochastic Approach to Control for Maximal Accuracy (pp. 1395-1396) San Diego, CA: 36th IEEE Conference on Decision and Control.
- Gray, W. S. and Mesko, J. (1997). General Input Balancing and Model Reduction for Linear and Nonlinear Systems European Control Conference.
- Gray, W. S. and Mesko, J. (1997). General Input Balancing Transformations for Nonlinear Systems (pp. 264-269) Baltimore, MD: Conference on Information Sciences and Systems.
- Lane, D., Gray, W. S. and Murphy, K. (1997). Linear H1 Optimal Control of a Two Degree of Freedom Magnetic Suspension System (pp. 1687-1691) Albuquerque, NM: American Control Conference.
- Scherpen, J. and Gray, W. S. (1997). On Minimality and Similarity Invariance Issues for Nonlinear Systems (pp. 63-93) Workshop: Mathematics for Systems.
- Hamsioglu, Z. and Gray, W. S. (1997). Velocity Estimation via a Neural Network Enhanced by Classical Detection Algorithms (pp. 896-901) Baltimore, MD: Conference on Information Sciences and Systems.
- Gray, W. S. and Mesko, J. (1996). Controllability and Observability Functions for Model Reduction of Nonlinear Systems (pp. 1244-1249) Princeton, NJ: Conference on Information Sciences and Systems.
- Gray, W. S. and Nabet, B. (1996). Volterra Series Analysis of a Neural Network for Velocity Estimation (pp. 926-931) Computational Engineering in Systems Applications, 1996 IMACS Multiconference.
- Bezick, S., Gray, W. S. and Rusnak, I. (1995). Application of Feedback Linearization to the Synthesis of Homing Guidance Laws (pp. 209-219) 35th Israel Annual Conference on Aerospace Sciences.
- Gray, W. S. and Verriest, E. (1995). Minimum Sensitivity Design via Gradient Flows Techniques (pp. 1091-1096) New Orleans, LA: 34th IEEE Conference on Decision and Control.
- Verriest, E. and Gray, W. S. (1995). Optimal Control for Maximal Accuracy with Arbitrary Control Space Metric (pp. 3914-3919) New Orleans, LA: 34th IEEE Conference on Decision and Control.
- Lane, D., McConnell, R., Gray, W. S. and Murphy, K. (1995). Robust Linear Controller Design for a Two-Degree of Freedom Magnetic Suspension System (pp. 273-278) Baltimore, MD: Conference on Information Sciences and Systems.
- Verriest, E. and Gray, W. S. (1994). A Geometric Approach to the Minimum Sensitivity Design Problem (pp. 518-523) Orlando, FL: 33rd IEEE Conference on Decision and Control.
- Lane, D., McConnell, R. and Gray, W. S. (1994). Force Modeling for the Control of a Two-Dimensional Magnetic Levitation System (pp. 149-152) Piscataway, NJ: IEEE Regional NY/NJ Control Conference.
- Gray, W. S. (1994). Modeling and Performance Tradeoffs for Sliding Mode Control of a Magnetic Suspension System (pp. 141-144) Piscataway, NJ: 1994 IEEE Regional NY/NJ Control Conference.
- McConnell, R. and Gray, W. S. (1994). Sliding Mode Control of a Magnetic Suspension System Using Sampled-Data (pp. 426-430) Princeton, NJ: Conference on Information Sciences and Systems.
- Bezick, S., Rusnak, I. and Gray, W. S. (1993). Design of Guidance Law for Homing Missile via Feedback Linearization (pp. 729-733) 1st IEEE Regional Conference on Aerospace Control Systems.
- Bezick, S., Rusnak, I. and Gray, W. S. (1993). Feedback Linearizing Control for the Guidance of a Homing Missile (pp. 393-398) Baltimore, MD: Conference on Information Sciences and Systems.
- Rusknak, I., Gray, W. S. and Guez, A. (1993). Generalizing the Certainty Equivalence Principle and Separation Theorems Beyond the Usual Heuristics (pp. 2965-2966) San Francisco, CA: American Control Conference.
- Goodman, S. and Gray, W. S. (1992). A Theorem on Maximum Entropy Compression of Ergodic sequences (pp. 873-877) Princeton, NJ: Conference on Information Sciences and Systems.
- Mercurio, S., Rusnak, I., Gray, W. S. and Kam, M. (1992). Controlling a Magnetic Levitation System via Feedback Linearization (pp. 1030-1035) Princeton, NJ: Conference on Information Sciences and Systems.
- Kam, M., Zhu, Q. and Gray, W. S. (1991). On Distributed Detection with Correlated Local Detectors (pp. 2174-2175) Boston, MA: American Control Conference.
- Kimber, R. and Gray, W. S. (1991). On Sampled-Data Implementations of Feedback Linearizing Controllers (pp. 1873-1874) 30th IEEE Conference on Decision and Control.
- Kimber, R. and Gray, W. S. (1991). The Effects of Sampling on Feedback Linearization: A Case Study (pp. 1059-1060) Boston, MA: American Control Conference.
- Gray, W. S., Verriest, E. and Lewis, F. (1990). A Hankel Matrix Approach to Singular System Realization Theory (pp. 73-78) Honolulu, HI: 29th IEEE Conference on Decision and Control.
- Goodman, S., Gray, W. S. and Brook, M. (1990). A Novel Neural Network for Temporal Pattern Identification with Applications to Control Systems (pp. 473-478) Philadelphia, PA: 5th IEEE International Symposium on Intelligent Control.
- Gray, W. S. and Verriest, E. (1989). On the Sensitivity of Generalized State-Space Systems (pp. 1337-1342) Tampa, FL: 28th IEEE Conference on Decision and Control.
- Gray, W. S. and Verriest, E. (1987). Optimality Properties of Balanced Realizations: Minimum Sensitivity (pp. 124-128) Los Angeles, CA: 26th IEEE Conference on Decision and Control.

## Presentations

- Gray, W. S. and Thitsa, M. ( 2009). Nonlinear System Interconnections and Integer Sequences SIAM Conference on Control and its Applications Denver, Colorado.
- Gray, W. S. ( 2008). Recoverable Flight Control Systems for Harsh Environments NASA Aviation Safety Conference Denver, CO.
- Gray, W. S. ( 2008). Design and Analysis of Recoverable Flight Control Systems for Harsh Environments - NRA Grant NNX07AD52A NASA Langley Research Center and broadcast to other NASA centers Hampton, VA.
- Gray, W. S. ( 2007). Design and Analysis of Recoverable Flight Control Systems for Harsh Environments via the SPIDER Architecture - NRA Grant NNX07AD52A presented at the NASA Langley and broadcast to other NASA centers Hampton, VA.
- Gray, W. S. and Herencia, H. ( 2006). Invariant Measures of Nonlinear Sampled-Data Systems with a Jump Linear Controlle 9th International Workshop on Hybrid Systems: Computation and Control Santa Barbara, CA.
- Gray, W. S. ( 2005). Performance Analysis and Validation of a Recoverable Flight Control System in a Neutron Environment University of New Mexico Albuquerque, New Mexico.
- Gray, W. S. ( 2003). Stability and Performance Measures for Recoverable Flight Control Systems Subject to Neutron-Induced Upsets Single Aircraft Accident Prevention Government/Industry Meeting Hampton, VA.
- Gray, W. S. ( 2001). Program Overview: Modeling and Control in Electromagnetic Environments (EME’s) NASA Langley Research Center Hampton, VA.
- Gray, W. S. ( 2001). Hankel Structures for Nonlinear Input-Output Systems The Technical University of Delft The Netherlands.
- Gray, W. S. ( 1999). General Input Balancing and Model Reduction for Linear and Nonlinear Systems Control and Dynamical Systems Lecture Series of the Institute for Systems Research, University of Maryland College Park, MD.
- Gray, W. S. ( 1998). Modeling Electromagnetic Disturbances in Closed-Loop Computer Controlled Flight Systems Old Dominion University Norfolk, VA.
- Gray, W. S. ( 1998). Volterra Series Analysis and Synthesis of a Neural Network for Computer Vision The University of Calgary Calgary, Canada.
- Gray, W. S. ( 1997). Sufficient Conditions for Minimality of a Nonlinear Realization via Controllability and Observability Functions Center for Dynamical Systems and Nonlinear Studies, The School of Mathematics, The Georgia Institute of Technology Atlanta, GA.
- Gray, W. S. ( 1997). Volterra Series Synthesis and Analysis of a Neural Network for Computer Vision Old Dominion University Norfolk, VA.
- Gray, W. S. ( 1997). State Space Model Reduction Methods for Nonlinear Control Systems The Technical University of Delft The Netherlands.
- Gray, W. S. ( 1996). Riemannian Maximal Accuracy Control International Symposium of Networks and Systems St. Louis, MO.
- Gray, W. S. ( 1996). General Input Balancing and Model Reduction for Linear and Nonlinear Systems Old Dominion University Norfolk, VA.
- Gray, W. S. ( 1995). Minimum Sensitivity Design for Nonlinear Input-Output Systems ETH-Zentrum Zurich, Switzerland.
- Gray, W. S. ( 1995). Geometric Nonlinear Control Theory for Navigation and Guidance Applications Galaxy Scientific Corporation Warminster, Pennsylvania.
- Gray, W. S. ( 1994). Geometric Nonlinear Control Theory and Its Applications Applied Physics Laboratory, Johns Hopkins University Baltimore, Maryland.
- Gray, W. S. ( 1992). Input-OutputMaps and Realization Theory, Part I: Fliess Functional Expansions in Continuous-Time NASA Langley Research Center Hampton, VA.
- Gray, W. S. ( 1992). Input-OutputMaps and Realization Theory, Part II: Fliess Functional Expansions in Discrete-Time NASA Langley Research Center Hampton, VA.
- Gray, W. S. ( 1989). A Geometric Approach to the Parametric Sensitivity of Dynamical Systems School of Electrical Engineering, Georgia Institute of Technology Atlanta, GA.

- Awarded membership in honor societies Eta Kappa Nu, Electrical Engineering, Pi Mu Epsilon, Mathematics, Pi Eta Sigma, Scholastics, Sigma Xi, Scientific Research, Tau Beta Pi, Engineering ,
- 2006: Best Paper in Session Award On the Markov Property for Nonlinear Discrete-Time Systems with Markovian Inputs’ (with A. Tejada and O. R. Gonzalez), 2006 American Control Conference
- 2005: Best Paper in Session Award for ‘Performance Analysis of Recoverable Flight Control Systems Using Hybrid Dynamical Models’ (with H. Zhang and O. R. Gonzalez), 2005 American Control Conference
- 2005: Outstanding Research Award, Department of Electrical and Computer Engineering, Old Dominion University
- 2003: Best Paper in Session Award for ‘A Self-Adaptive Predictive Congestion Control Model for Extreme Networks’ (with Y. Li and M. Song), 2003 International Conference on Computer Communication and Control Technologies
- 2003: Excellence in Research Award, College of Engineering and Technology, Old Dominion University
- 2003: Outstanding Teaching Award, Department of Electrical and Computer Engineering, Old Dominion University
- 2002: Best Paper in Session Award for ‘Analysis of Design Tradeoffs in Rollback Recovery Methods for Fault Tolerant Digital Control Systems’ (with O. R. Gonz´alez and A. Tejada), American Control Conference
- 2002: Best SAE Technical Paper in 2001 for ‘Analytical Tools for the Design and Verification of Safety Critical Control Systems’ (with O. R. Gonz´alez and A. Tejada), SAE Transactions Journal of Aerospace
- 1999: Best Paper in Session Award for ‘Digital Linear State Feedback Control Subject to Electromagnetic Disturbances’ (with O. R. Gonzalez and M. Dogan), American Control Conference
- 1999: Best Paper in Session Award for ‘On Singular Value Functions and Hankel Operators for Nonlinear Systems’ (with J. M. A. Scherpen), American Control Conference
- 1998: Best Paper in Session Award for ‘Modeling Electromagnetic Disturbances in Closed-Loop Computer Controlled Flight Systems’ (with O. R. Gonzalez), American Control Conference
- 1998: Best Paper in Session Award for ‘Sufficient Conditions for Minimality of a Nonlinear Realization via Controllability and Observability Functions’ (with J. M. A. Scherpen), American Control Conference
- 1997: Visiting Scholar, Delft Institute of Technology, The Netherlands
- 1992: NASA-ASEE Summer Faculty Fellowship, NASA Langley Research Center
- 1991: Research Scholar Award, Drexel University
- 1989: Outstanding Graduate Teaching Assistant Award, Georgia Tech
- 1988: Schlumberger Foundation Fellowship, Georgia Tech
- 1986: TRW Augmentation Fellowship, Georgia Tech
- 1984: The President’s Fellowship, Georgia Tech
- 1983: Nominated for the Henry Ford II Scholarship, Purdue University
- 1982: Atlantic Richfield’s Academic Excellence Award, Purdue University
- 1981: Alcoa Foundation Scholarship, Purdue University, Purdue University
- 1981: Alcoa Foundation Scholarship, Purdue University, Tau Beta Pi, Purdue University
- 1981: Purdue Distinguished Student Award, Purdue University