Robust H/sub /spl infin// filter design of uncertain descriptor systems with discrete and distributed delays

The robust H/sub /spl infin// filtering problem for a class of continuous-time uncertain linear descriptor systems with time-varying discrete and distributed delays is investigated. The time delays are assumed to be constant and known. The uncertainties under consideration are norm-bounded, and possible time-varying, uncertainties. Sufficient condition for the existence of an H/sub /spl infin// filter is expressed in terms of strict linear matrix inequalities (LMIs). Instead of using decomposition technique, a unified form of LMIs is proposed to show the exponential stability of the augmented systems. The condition for assuring the stability of the "fast" subsystem is implied from the unified form of LMIs, which is shown to be less conservative than the characteristic equation based conditions or matrix norm-based conditions. The suitable filter is derived through a convex optimization problem. A numerical example is given to show the effectiveness of the method.

[1]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[2]  D.L. Elliott,et al.  Feedback systems: Input-output properties , 1976, Proceedings of the IEEE.

[3]  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..

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

[5]  D. McFarlane,et al.  Optimal guaranteed cost control and filtering for uncertain linear systems , 1994, IEEE Trans. Autom. Control..

[6]  L. Dai.  Filtering and LQG problems for discrete-time stochastic singular systems , 1989 .

[7]  J. Speyer,et al.  A Linear-Quadratic Game Approach to Estimation and Smoothing , 1991, 1991 American Control Conference.

[8]  Minyue Fu,et al.  A linear matrix inequality approach to robust H∞ filtering , 1997, IEEE Trans. Signal Process..

[9]  Patrizio Colaneri,et al.  Guaranteed H∞ robustness bounds for Wiener filtering and prediction , 2002 .

[10]  Lihua Xie,et al.  Robust Kalman filtering for uncertain systems , 1994 .

[11]  Thomas B. Sheridan,et al.  Remote Manipulative Control with Transmission Delay , 1963 .

[12]  Shengyuan Xu,et al.  Robust stability and stabilization for singular systems with state delay and parameter uncertainty , 2002, IEEE Trans. Autom. Control..

[13]  A. Ichikawa,et al.  H/sub /spl infin//-control for Takagi-Sugeno fuzzy descriptor systems , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[14]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  Mohamed Darouach,et al.  Kalman filtering for continuous descriptor systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[16]  Pramod P. Khargonekar,et al.  FILTERING AND SMOOTHING IN AN H" SETTING , 1991 .

[17]  Pramod P. Khargonekar,et al.  Mixed H2/H∞ filtering , 1996 .

[18]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

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

[20]  Emilia Fridman,et al.  Robust H∞ filtering of linear systems with time-varying delay , 2003, IEEE Trans. Autom. Control..

[21]  U. Shaked,et al.  Game theory approach to optimal linear estimation in the minimum H/sup infinity /-norm sense , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[22]  Emilia Fridman,et al.  A new H∞ filter design for linear time delay systems , 2001, IEEE Trans. Signal Process..

[23]  E. Fridman,et al.  H∞-control of linear state-delay descriptor systems: an LMI approach , 2002 .

[24]  Emilia Fridman,et al.  Robust H∞ control of distributed delay systems with application to combustion control , 2001, IEEE Trans. Autom. Control..

[25]  Uri Shaked,et al.  A dynamic game approach to mixedH∞/H2 estimation , 1996 .

[26]  Jean C. Walrand,et al.  High-performance communication networks , 1999 .

[27]  Zidong Wang,et al.  Robust filtering for uncertain linear systems with delayed states and outputs , 2002 .

[28]  Bruce A. Francis,et al.  Limited Data Rate in Control Systems with Networks , 2002 .

[29]  P. Khargonekar,et al.  Filtering and smoothing in an H/sup infinity / setting , 1991 .

[30]  M. Malek-Zavarei,et al.  Time-Delay Systems: Analysis, Optimization and Applications , 1987 .

[31]  Mohamed Darouach,et al.  State estimation of stochastic singular linear systems , 1993 .

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

[33]  Uri Shaked,et al.  𝒽∞ Filtering for Continuous-time Linear Systems with Delay , 1999, IEEE Trans. Autom. Control..

[34]  Tatsuo Furuno,et al.  Multipath propagation model for line-of-sight street microcells in urban area , 2000, IEEE Trans. Veh. Technol..

[35]  I. Yaesh,et al.  Game theory approach to optimal linear estimation in minimum H_∞-norm sense , 1989 .

[36]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .