Overview

  • 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.

    • Selected Publications

    Articles In Academic Journals

    Year Title
    2018 Stability, performance and sensitivity analysis of I.I.D. Jump linear systems.  International Journal of Control. 1460-1472.
    2013 Stability Analysis of Stochastic Hybrid Jump Linear Systems Using a Markov Kernel Approach.  IEEE Transactions on Automatic Control. 3156-3168.
    2013 Tracking Performance of Distributed Recoverable Flight Control Systems Subject to High Intensity Radiated Fields.  IEEE Transactions on Aerospace and Electronic Systems. 521-542.
    2012 On Fliess Operators Driven by L2-Ito Processes.  Stochastics: An International Journal of Probability and Stochastic Processes. 507-532.
    2012 On the Radius of Convergence of Interconnected Analytic Nonlinear Systems.  SIAM Journal on Control and Optimization. 2786-2813.
    2009 Bilinear System Interconnections and Generating Series of Weighted Petri Nets.  Systems and Control Letters. 841-848.
    2008 Noncausal Fliess Operators and Their Shuffle Algebra.  International Journal of Control special issue for the occasion of M. Fliess’s 60th birthday). 344-357.
    2008 Output Tracking Performance of a Recoverable Digital Flight Control System in Neutron Environments.  IEEE Transactions on Aerospace and Electronic Systems.
    2008 Performance Analysis of Digital Flight Control Systems with Rollback Error Recovery Subject to Simulated Neutron-Induced Upsets.  IEEE Transactions on Control Systems Technology. 46-59.
    2008 Stability of Digital Control Systems Implemented in Error-Recoverable Computers.  International Journal of Control. 1665-1681.
    2008 Tracking Performance of a Recoverable Flight Control System in Neutron Environments.  IEEE Transactions on Aerospace and Electronic Systems. 321-335.
    2006 Balanced Realizations Near Stable Invariant Manifolds.  Automatica. 653-659.
    2006 The Formal Laplace-Borel Transform of Fliess Operators and the Composition Product.  International Journal of Mathematics and Mathematical Sciences. 1-14.
    2005 Generating Series for Interconnected Analytic Nonlinear Systems.  SIAM Journal on Control and Optimization. 646-672.
    2005 Hankel Singular Value Functions from Schmidt Pairs for Nonlinear Input-Output Systems.  Systems and Control Letters. 135-144.
    2004 Book Review: Nonlinear System Identification – Input-Output Modeling Approach, Volumes 1&2 by R. Haber and L. Keviczky.  Automatica. 901-903.
    2002 Analytical Tools for the Design and Verification of Safety Critical Control Systems.  2001 SAE Transactions - Journal of Aerospace. 481-490.
    2002 Fliess Operators on Lp Spaces: Convergences and Continuity.  Systems and Control Letters. 67-74.
    2002 Hamiltonian Realizations of Nonlinear Adjoint Operators.  Automatica. 1769-1775.
    2002 Nonlinear Hilbert Adjoints: Properties and Applications to Hankel Singular Value Analysis.  Nonlinear Analysis: Theory, Methods & Applications. 883-901.
    2001 On the Nonuniqueness of Singular Value Functions and Balanced Nonlinear Realizations.  Systems and Control Letters. 219-232.
    2000 Minimality and Local State Decompositions of a Nonlinear State Space Realization Using Energy Functions.  IEEE Transactions on Automatic Control. 2079-2086.
    2000 Stability Analysis of Digital Linear Flight Controllers Subject to Electromagnetic Disturbances.  IEEE Transactions on Aerospace and Electronic Systems. 1204-1218.
    1999 Observability Functions for Linear and Nonlinear Systems.  Systems and Control Letters. 99-113.
    1999 Volterra Series Analysis and Synthesis of a Neural Network for Velocity Estimation.  IEEE Transactions on Systems, Man, and Cybernetics. 190-197.
    1995 A Geometric Approach to the Minimum Sensitivity Design Problem.  SIAM Journal on Control and Optimization. 863-881.
    1995 Guidance of a Homing Missile Via Nonlinear Geometric Control Methods.  AIAA Journal of Guidance, Control, and Dynamics. 441-448.
    1992 Optimal Data Fusion of Correlated Local Decisions in Multiple Sensor Detection Systems.  IEEE Transactions on Aerospace and Electronic Systems. 916-920.
    1991 High-Performance DSP Architectures for Intelligence and Control Applications.  IEEE Control Systems Magazine. 49-55.

    Conference Papers

    Year Title
    2017 Data-driven siso predictive control using adaptive discrete-time fliess operator approximations
    2017 Integration of output tracking and trajectory generation via analytic left inversion
    2012 On the radius of convergence of cascaded analytic nonlinear system
    2011 Experimental Validation of a Performance Model for a Distributed Recoverable Boeing 747 Flight Control System Subject to Digital Upsets.  13-19.
    2011 On the Radius of Convergence of Cascaded Analytic Nonlinear Systems
    2010 High-Intensity Radiated Field Fault-Injection Experiment for a Fault-Tolerant Distributed Communication System.  4.E.3.
    2010 On the Absolute Global Convergence of Fliess Operators Driven by L2-Itô Processes.  280-285.
    2010 On the Radius of Convergence of Self-excited Feedback Connected Analytic Nonlinear Systems
    2010 Performance Analysis of Fault Tolerant Control Systems with I.I.D. Upsets.  6197-6204.
    2010 Tracking Performance Analysis of a Distributed Recoverable Boeing 747 Flight Control System Subject to Digital Upsets.  548-554.
    2009 On Fliess Operators Driven by L2-Itô Random Processes.  7478-7484.
    2009 Transformations of Markov Processes in Fault Tolerant Interconnected Systems.  227-232.
    2008 A Performance Model for a Distributed Flight Control System Subject to Random Upsets.  918-923.
    2008 Formal Fliess Operators with Applications to Feedback Interconnections
    2008 Mean Square Stability Analysis of Sampled-Data Supervisor Control Systems.  37-42.
    2008 Towards a Metric for the Assessment of Safety Critical Control Systems.  Paper AIAA 2008-6804.
    2008 Transformations of Markov Processes in Fault Tolerant Interconnected Systems
    2007 A Black-Scholes Approach to Satisfying the Demand in a Failure-Prone Manufacturing System.  154-158.
    2007 Dynamically Colored Petri Net Representation of Nonlinear Sampled-Data Systems with Embedded Recovery Algorithms.  97-102.
    2007 Mean Square Stability Analysis of Hybrid Jump Linear Systems Using a Markov Kernel Approach.  3482-3487.
    2007 On the Bilinearity of Cascaded Bilinear Systems.  5581-5587.
    2007 On the Rationality of the Composition Product: A Survey.  238-243.
    2007 Stability Analysis of Hybrid Jump Linear Systems with Markov Inputs.  6280-6285.
    2006 A Measure-Theoretic Proof of the Markov Property for Hybrid Systems with Markovian Inputs.  328-332.
    2006 Algebraically Defined Gramians for Nonlinear Systems.  3730-3735.
    2006 Geometry and Topology of the State Space via Balancing.  840-848.
    2006 Markovian Statistical Data Analysis of Single-Event Upsets Triggered by High Intensity Neutrons.  349-353.
    2006 Noncausal Fliess Operators and Their Shuffle Algebra.  2805-2813.
    2006 On the Markov Property for Nonlinear Discrete-Time Systems with Markovian Inputs.  899-904.
    2006 Towards a Theory of Sampled-Data Piecewise-Deterministic Markov Processes.  944-949.
    2005 Asymptotic and Mean Square Stability Conditions for Hybrid Jump Linear System with Performance Supervision.  569-574.
    2005 Asymptotic and Mean Square Stability Conditions for Hybrid Jump Linear Systems with Performance Supervision.  569-574.
    2005 Local Convergence of the Feedback Product via the Asymptotics of the Catalan Numbers.  6140-6145.
    2005 On Feedback Connections of Analytic Nonlinear Systems and Combinatorics on Words.  429-434.
    2005 Performance Analysis and Validation of a Recoverable Flight Control System in a Simulated Neutron Environment.  Paper 2005-6430.
    2005 Performance Analysis of Recoverable Flight Control Systems Using Hybrid Dynamical Models.  2787-2792.
    2004 Balanced Nonlinear Realizations.  1164-1169.
    2004 Balanced Realizations Near Stable Invariant Manifolds
    2004 Markov Jump-Linear Performance Models for Recoverable Flight Control Computers.  408-412.
    2004 On the Stability of Jump-Linear Systems Driven by Finite-State Machines with Markovian Inputs.  2534-2539.
    2004 On the stability of Jump-Linear System Driven by Finite-State Machines with Markovian Inputs.  2534-2539.
    2004 Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Contoller.  4128-4133.
    2004 Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller.  4128-413.
    2004 Stochastic Stability of Sampled Data Systems with a Jump Linear Controller.  256-260.
    2004 The Formal Laplace-Borel Transform, Fliess Operators and the Composition Product.  333-337.
    2004 Towards Stability Analysis of Jump Linear Systems with State-Dependent and Stochastic Switching.  1893-1898.
    2003 A Self-adaptive Predictive Congestion Control Model for Extreme Networks.  327-332.
    2003 Closed-Loop Performance Measures for Flight Controllers Subject to Neutron-Induced Upsets.  2465-2470.
    2003 Closed-Loop Performance for Flight Controllers Subject to Neutron-Induced Upsets.  2465-2470.
    2003 Neutron Particle Effects on a Quad-Redundant Flight Control Computer.  1.B.2-1–8.
    2003 Stochastic Stability of a Recoverable Computer Control System Modeled as a Finite-State Machine.  2240-2245.
    2002 Analysis of Design Tradeoffs in Rollback Recovery Methods for Fault Tolerant Digital Control Systems.  4801-4806.
    2002 Fliess Operators in Cascade and Feedback Systems.  173-178.
    2002 Generating Series for Nonlinear Cascade and Feedback Systems.  2720-2725.
    2002 Hankel Singular Value Functions from Schmidt Pairs for Nonlinear Input-Output Systems.  3540-3545.
    2002 Interconnected Systems of Fliess Operators
    2002 Towards Hybrid Models of Recoverable Computer Control Systems.  13.C.2.
    2001 Analytical Tools for the Design and Verification of Safety Critical Control Systems
    2001 Computing Hilbert Adjoints of Fliess Operators.  481-486.
    2001 Discrete-Time Nonlinear Balancing.  515-520.
    2001 Nonlinear Adjoints of Fliess Operators.  2625-2630.
    2001 Nonlinear Balanced Realizations.  3250-3251.
    2001 Nonlinear Hilbert Adjoints: Properties and Applications to Hankel Singular Value Analysis.  3582-3587.
    2001 Stability Analysis of Electromagnetic Interference Upset Recovery Methods.  4134-4139.
    2001 Stability Analysis of Upset Recovery Methods for Electromagnetic Interference.  1.C.4-1–9.
    2000 Analysis of Memory Bit Errors Induced by Electromagnetic Interference in Closed-Loop Digital Flight Control Systems.  3.C.5.
    2000 Design of a Magnetic Suspension and Balance System for the Princeton/ONR High Reynolds Number Testing Facility.  675-683.
    2000 Fliess Operators on Lp Spaces: Convergence and Continuity.  4385-4390.
    2000 Flow Balancing Nonlinear Systems
    2000 Hamiltonian Extensions, Hilbert Adjoints and Singular Value Functions for Nonlinear Systems.  5102-5107.
    2000 Hamiltonian Realizations of Nonlinear Adjoint Operators.  39-44.
    2000 On Adjoints and Singular Value Functions for Nonlinear Systems.  FP8.
    2000 Properties of Fliess Operators on Lp-Spaces.  FP8.
    2000 Stability of Digital Control Systems Subject to Jump Linear Random Perturbations.  1154-1159.
    2000 State Dependent Matrices and Balanced Energy Functions for Nonlinear Systems
    1999 Balancing Nonlinear Systems Near Attracting Invariant Manifolds
    1999 Digital Linear State Feedback Control Subject to Electromagnetic Disturbances.  3500-3504.
    1999 Hankel Structure for Nonlinear Input-Output Systems and State-Space Realizations.  331-363.
    1999 Modeling the Nonlinear Mapping in a Neural Based Motion Detector.  245-252.
    1999 On the Nonuniqueness of Balanced Nonlinear Realizations.  4736-4741.
    1999 On the Nonuniqueness of Singular Value Functions in Balanced Nonlinear Realizations.  729-734.
    1999 Stochastic Perturbation Analysis of Computer Control Systems Subject to Electromagnetic Disturbances.  1797-1802.
    1999 Stochastic Perturbation Models of Electromagnetic Disturbances in Closed-Loop Computer Controlled Flight Systems.  10.C.4.
    1998 EMI Models for Controller Analysis and Synthesis
    1998 Energy Functions and Algebraic Gramians for Bilinear Systems.  103-108.
    1998 Hankel Operators and Gramians for Nonlinear Systems.  1416-1421.
    1998 Modeling Electromagnetic Disturbances in Closed-Loop Computer Controlled Flight Systems.  359-364.
    1997 A Stochastic Approach to Control for Maximal Accuracy.  1395-1396.
    1997 General Input Balancing Transformations for Nonlinear Systems.  264-269.
    1997 General Input Balancing and Model Reduction for Linear and Nonlinear Systems
    1997 Linear H1 Optimal Control of a Two Degree of Freedom Magnetic Suspension System.  1687-1691.
    1997 On Minimality and Similarity Invariance Issues for Nonlinear Systems.  63-93.
    1997 Velocity Estimation via a Neural Network Enhanced by Classical Detection Algorithms.  896-901.
    1996 Controllability and Observability Functions for Model Reduction of Nonlinear Systems.  1244-1249.
    1996 Volterra Series Analysis of a Neural Network for Velocity Estimation.  926-931.
    1995 Application of Feedback Linearization to the Synthesis of Homing Guidance Laws.  209-219.
    1995 Minimum Sensitivity Design via Gradient Flows Techniques.  1091-1096.
    1995 Optimal Control for Maximal Accuracy with Arbitrary Control Space Metric.  3914-3919.
    1995 Robust Linear Controller Design for a Two-Degree of Freedom Magnetic Suspension System.  273-278.
    1994 A Geometric Approach to the Minimum Sensitivity Design Problem.  518-523.
    1994 Force Modeling for the Control of a Two-Dimensional Magnetic Levitation System.  149-152.
    1994 Modeling and Performance Tradeoffs for Sliding Mode Control of a Magnetic Suspension System.  141-144.
    1994 Sliding Mode Control of a Magnetic Suspension System Using Sampled-Data.  426-430.
    1993 Design of Guidance Law for Homing Missile via Feedback Linearization.  729-733.
    1993 Feedback Linearizing Control for the Guidance of a Homing Missile.  393-398.
    1993 Generalizing the Certainty Equivalence Principle and Separation Theorems Beyond the Usual Heuristics.  2965-2966.
    1992 A Theorem on Maximum Entropy Compression of Ergodic sequences.  873-877.
    1992 Controlling a Magnetic Levitation System via Feedback Linearization.  1030-1035.
    1991 On Distributed Detection with Correlated Local Detectors.  2174-2175.
    1991 On Sampled-Data Implementations of Feedback Linearizing Controllers.  1873-1874.
    1991 The Effects of Sampling on Feedback Linearization: A Case Study.  1059-1060.
    1990 A Hankel Matrix Approach to Singular System Realization Theory.  73-78.
    1990 A Novel Neural Network for Temporal Pattern Identification with Applications to Control Systems.  473-478.
    1989 On the Sensitivity of Generalized State-Space Systems.  1337-1342.
    1987 Optimality Properties of Balanced Realizations: Minimum Sensitivity.  124-128.

    Research Overview

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

    • Grants

  • Design and Analysis of Recoverable Flight Control Systems for Harsh Environments via the SPIDER Architecture  awarded by NASA Langley Research Center Cooperative Agreement NNX07AD52A 2007 - 2012
  • Advanced Concepts for Recoverable Controllers in Safety Critical Systems  awarded by NASA Langley Research Center Cooperative Agreement NNL04AA03A 2004 - 2007
  • System Level Effects of Neutron Induced Single Event Upsets on Recoverable Digital Control Systems  awarded by NASA Langley Research Center Cooperative Agreement NCC-1-03026 2003 - 2006
  • Hybrid Modeling and Analysis of Error Recovery in Safety Critical Flight Control Systems  awarded by National Science Foundation Grant CCR-0209094 2002 - 2005
  • Supplement to ODURF Project #101831  awarded by NASA Langley Research Center NCC-1-392, Supplement 2002 - 2003
  • Stochastic Dynamical Models for Digital Control Systems in Electromagnetic Environments  awarded by NASA Langley Research Center Cooperative Agreement NCC-1-392 2000 - 2003
  • Robust Stability and Performance of a Closed-Loop Computer Control System Subject to Electromagnetic Disturbances  awarded by NASA Langley Research Center Grant NAS-1-99093 1999 - 2000
  • Supplemental Funds for Characterization, Control and Commissioning of the Magnetic Suspension and Balance System for the Princeton/ONR High Reynolds Number Testing Facility  awarded by Princeton University Grant 150-67555-1 1999 - 2000
  • Characterization, Control and Commissioning of the Magnetic Suspension and Balance System for the Princeton/ONR High Reynolds Number Testing Facility  awarded by Office of Naval Research Grant N00014-99-1-0298 1998 - 2000
  • Balancing and Model Reduction for Nonlinear Dynamical Systems  awarded by North Atlantic Treaty Organization - NATO Country Cooperative Research Grant CRG-97113 1997 - 1999
  • Stability Analysis and Augmentation of a Closed-Loop Computer Control System Subject to Electromagnetic Disturbances  awarded by NASA Langley Research Center Grant NAS-1-19858 1997 - 1998
  • Neural Control of Magnetic Suspension Systems for Aerospace Applications  awarded by NASA Langley Research Center Grant 1993 - 1994
  • Engineering Issues in Designing Feedback Linearizing Controllers  awarded by Drexel University - Research Scholar Award 1991
  • Performance Analysis and Validation of High Efficiency Error Recovery Algorithms for Safety Critical Systems  awarded by National Science Foundation 2005 -
  • Center for Photon Engineering of Materials and Systems  awarded by National Science Foundation 2000 -

    • Education And Training

  • 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

    • Full Name

  • William Gray