Robust H1 Filtering for Discrete Stochastic Time-Delay Systems with Nonlinear Disturbances*

This paper deals with the problem of robust H1 filtering for dis- crete time-delay systems with stochastic perturbation and nonlinear distur- bance. It is assumed that the state-dependent noises and the nonlinearities satisfying global Lipschitz conditions enter into both the state and measure- ment equations, and the system matrices also contain parameter uncertainties residing in a polytope. Attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed noise attenuation level in an H1 sense with respect to all energy-bounded noise inputs for all admissible uncertainties and time delays. Sufficient conditions for the existence of such filters are formulated in terms of a set of linear matrix inequalities, upon which admissible filters can be obtained from the solution of a convex optimization problem. A numerical example is provided to illustrate the applicability of the developed filter design procedure.

[1]  Michael Basin,et al.  Integral approach to optimal filtering and control of continuous processes with time-varying delays , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[2]  X. Mao,et al.  Robust stability of uncertain stochastic differential delay equations , 1998 .

[3]  Reinaldo M. Palhares,et al.  Robust filtering with guaranteed energy-to-peak performance - an LM1 approach , 2000, Autom..

[4]  Pedro Luis Dias Peres,et al.  Robust H∞ filter design for uncertain linear systems with multiple time-varying state delays , 2001, IEEE Trans. Signal Process..

[5]  D. Williams.  STOCHASTIC DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS , 1976 .

[6]  M. Mahmoud,et al.  Robust stability, stabilization and ℋ∞ control of time‐delay systems with Markovian jump parameters , 2003 .

[7]  J. Lam,et al.  Delay-dependent robust H∞ control for uncertain systems with time-varying delays , 1998 .

[8]  Carlos S. Kubrusly,et al.  On discrete stochastic bilinear systems stability , 1986 .

[9]  Emilia Fridman,et al.  A descriptor system approach to H∞ control of linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[10]  Maurício C. de Oliveira,et al.  H2 and H∞ robust filtering for convex bounded uncertain systems , 2001, IEEE Trans. Autom. Control..

[11]  E. Boukas,et al.  Optimal guaranteed cost control of uncertain discrete time-delay systems , 2003 .

[12]  Hong Qiao,et al.  Robust filtering for bilinear uncertain stochastic discrete-time systems , 2002, IEEE Trans. Signal Process..

[13]  D. Hinrichsen,et al.  H∞-type control for discrete-time stochastic systems , 1999 .

[14]  D. Hinrichsen,et al.  Stochastic $H^\infty$ , 1998 .

[15]  X. Mao,et al.  Exponential stability of stochastic delay interval systems , 2000 .

[16]  Lihua Xie,et al.  Stabilization of a class of uncertain large-scale stochastic systems with time delays , 2000, Autom..

[17]  Shoudong Huang,et al.  H8 model reduction for linear time-delay systems: Continuous-time case , 2001 .

[18]  W. Wonham.  On a Matrix Riccati Equation of Stochastic Control , 1968 .

[19]  D. Hinrichsen,et al.  Stochastic H∞ , 1998 .

[20]  Ian R. Petersen,et al.  An LMI approach to output-feedback-guaranteed cost control for uncertain time-delay systems , 2000 .

[21]  Shengyuan Xu,et al.  Robust Filtering for a Class of Discrete-Time Uncertain Nonlinear Systems with State Delay , 2002 .

[22]  Magdi S. Mahmoud,et al.  Robust stability, stabilization and H-infinity control of time-delay systems with Markovian jump parameters , 2003 .

[23]  Shing-Tai Pan,et al.  Robust Kalman filter synthesis for uncertain multiple time-delay stochastic systems , 1996 .

[24]  Huijun Gao,et al.  Delay-dependent robust H∞ and L2-L∞ filtering for a class of uncertain nonlinear time-delay systems , 2003, IEEE Trans. Autom. Control..

[25]  U. G. Haussmann,et al.  Optimal Stationary Control with State Control Dependent Noise , 1971 .

[26]  Isaac Yaesh,et al.  Hinfinity control and filtering of discrete-time stochastic systems with multiplicative noise , 2001, Autom..

[27]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[28]  L. Guo.  H/sub /spl infin// output feedback control for delay systems with nonlinear and parametric uncertainties , 2002 .

[29]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .

[30]  Zikuan Liu,et al.  Robust H∞ filtering for polytopic uncertain time-delay systems with Markov jumps , 2002, Comput. Electr. Eng..

[31]  P. Peres,et al.  Robust filtering with guaranteed energy-to-peak performance — an LMI approach , 1999 .

[32]  PooGyeon Park,et al.  A delay-dependent stability criterion for systems with uncertain time-invariant delays , 1999, IEEE Trans. Autom. Control..

[33]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[34]  Keith J. Burnham,et al.  On designing observers for time-delay systems with non-linear disturbances , 2002 .