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.  Filtering and LQG problems for discrete-time stochastic singular systems , 1989 .

[2]  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,.

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

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

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

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

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

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

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

[10]  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..

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

[12]  Philippe Neveux,et al.  Robust filtering for uncertain systems , 2001, Signal Process..

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

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

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

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

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

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