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- W Steven Gray
- Associate Professor
- Electrical & Computer Engineering
- 231k Kaufman Hall
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Norfolk,
VA
23529
- 757-683-4671
- sgray@odu.edu
- Web Page
- 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.
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Education
- Georgia Institute Of Technology,
1989
- Major: Electrical Engineering
- Degree: Ph. D.
- Georgia Institute of Technology,
1988
- Major: Applied Mathematics
- Degree: M.S.
- Georgia Institute of Technology,
1985
- Major: Electrical Engineering
- Degree: M.S.
- Purdue University,
1983
- Major: Electrical Engineering
- Degree: B.S.
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Research Interests
- Formal power series methods for nonlinear systems analysis; realization theory and model
reduction for nonlinear systems; fault-tolerant control for safety critical systems.
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Books
- Gray, W. S. Formal Power Series Methods for Nonlinear Systems Analysis.
- Meystel, A., Herath, J., and Gray, W. S. (1990). Proceedings of the 5th IEEE International. IEEE Computer Society Press.
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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..
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Articles
- Gray, W. S., Wang, R., Chavez, J., and Gonzalez, O. A Performance Model for a Distributed Flight Control System Subject to Random Upsets. IEEE Transactions on Control Systems Technology
- Gray, W. S., and Thitsa, M. A Unified Approach to Generating Series for Cascaded Nonlinear Input-output Systems.
- Duffaut, L., Gray, W. S., and Gonzalez, O. Fliess Operators with Itˆo Process Inputs: Convergence and Continuity. Systems and Control Letters
- Gray, W. S., and Wang, Y. Formal Fliess Operators with Applications to Feedback Interconnections. ’Systems and Control Letters
- Gray, W. S., Herencia, H., and Duffaut, L. Interconnections of Bilinear Systems and Generating Series of Weighted Petri Nets. Systems and Control Letters
- Thitsa, M., and Gray, W. S. On the Radius of Convergence of Interconnected Analytic Nonlinear Systems.
- Herencia, H., Gonzalez, O., and Gray, W. S. Towards a Theory of Sampled-Data Piecewise-Deterministic Markov Processes. IEEE Transactions on Automatic Control
- Tejada, A., and Gray, W. S. (2010). On Nonlinear Discrete-Time Systems Driven by Markov Chains. Journal of the Franklin Institute, 347 (5), (pp. 795-805).
- 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).
- , I. T., 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).
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Presentations
- Nonlinear System Interconnections and Integer Sequences
- Conference Name: Algebraic Tools for Nonlinear Control
- Sponsoring Organization: Algebraic Tools for Nonlinear Control
- Location: Denver, Colorado
- Date: 2009
- Authors/Presenters:
Gray, W. S.
Thitsa, M.
- Recoverable Flight Control Systems for Harsh Environments
- Conference Name:
- Location: Denver, CO
- Date: 2008
- Authors/Presenters:
Gray, W. S.
- Design and Analysis of Recoverable Flight Control Systems for Harsh Environments - NRA Grant NNX07AD52A
- Conference Name:
- Location: Hampton, VA
- Date: 2008
- Authors/Presenters:
Gray, W. S.
- Design and Analysis of Recoverable Flight Control Systems for Harsh Environments via the SPIDER Architecture - NRA Grant NNX07AD52A
- Conference Name:
- Location: Hampton, VA
- Date: 2007
- Authors/Presenters:
Gray, W. S.
- Invariant Measures of Nonlinear Sampled-Data Systems with a Jump Linear Controlle
- Conference Name:
- Location: Santa Barbara, CA
- Date: 2006
- Authors/Presenters:
Gray, W. S.
Herencia, H.
- Performance Analysis and Validation of a Recoverable Flight Control System in a Neutron Environment
- Conference Name:
- Location: Albuquerque, New Mexico
- Date: 2005
- Authors/Presenters:
Gray, W. S.
- Stability and Performance Measures for Recoverable Flight Control Systems Subject to Neutron-Induced Upsets
- Conference Name:
- Location: Hampton, VA
- Date: 2003
- Authors/Presenters:
Gray, W. S.
- Program Overview: Modeling and Control in Electromagnetic Environments (EME’s)
- Conference Name:
- Location: Hampton, VA
- Date: 2001
- Authors/Presenters:
Gray, W. S.
- Hankel Structures for Nonlinear Input-Output Systems
- Conference Name:
- Location: The Netherlands
- Date: 2001
- Authors/Presenters:
Gray, W. S.
- General Input Balancing and Model Reduction for Linear and Nonlinear Systems
- Conference Name:
- Location: College Park, MD
- Date: 1999
- Authors/Presenters:
Gray, W. S.
- Modeling Electromagnetic Disturbances in Closed-Loop Computer Controlled Flight Systems
- Conference Name:
- Location: Norfolk, VA
- Date: 1998
- Authors/Presenters:
Gray, W. S.
- Volterra Series Analysis and Synthesis of a Neural Network for Computer Vision
- Conference Name:
- Location: Calgary, Canada
- Date: 1998
- Authors/Presenters:
Gray, W. S.
- Sufficient Conditions for Minimality of a Nonlinear Realization via Controllability and Observability Functions
- Conference Name:
- Location: Atlanta, GA
- Date: 1997
- Authors/Presenters:
Gray, W. S.
- Volterra Series Synthesis and Analysis of a Neural Network for Computer Vision
- Conference Name:
- Location: Norfolk, VA
- Date: 1997
- Authors/Presenters:
Gray, W. S.
- State Space Model Reduction Methods for Nonlinear Control Systems
- Conference Name:
- Location: The Netherlands
- Date: 1997
- Authors/Presenters:
Gray, W. S.
- Riemannian Maximal Accuracy Control
- Conference Name:
- Location: St. Louis, MO
- Date: 1996
- Authors/Presenters:
Gray, W. S.
- General Input Balancing and Model Reduction for Linear and Nonlinear Systems
- Conference Name:
- Location: Norfolk, VA
- Date: 1996
- Authors/Presenters:
Gray, W. S.
- Minimum Sensitivity Design for Nonlinear Input-Output Systems
- Conference Name:
- Location: Zurich, Switzerland
- Date: 1995
- Authors/Presenters:
Gray, W. S.
- Geometric Nonlinear Control Theory for Navigation and Guidance Applications
- Conference Name:
- Location: Warminster, Pennsylvania
- Date: 1995
- Authors/Presenters:
Gray, W. S.
- Geometric Nonlinear Control Theory and Its Applications
- Conference Name:
- Location: Baltimore, Maryland
- Date: 1994
- Authors/Presenters:
Gray, W. S.
- Input-OutputMaps and Realization Theory, Part I: Fliess Functional Expansions in Continuous-Time
- Conference Name:
- Location: Hampton, VA
- Date: 1992
- Authors/Presenters:
Gray, W. S.
- Input-OutputMaps and Realization Theory, Part II: Fliess Functional Expansions in Discrete-Time
- Conference Name:
- Location: Hampton, VA
- Date: 1992
- Authors/Presenters:
Gray, W. S.
- A Geometric Approach to the Parametric Sensitivity of Dynamical Systems
- Conference Name:
- Location: Atlanta, GA
- Date: 1989
- Authors/Presenters:
Gray, W. S.
- 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
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Contracts, Grants and Sponsored Research