Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays

This paper considers the problem of robust H/sup /spl infin// filtering for uncertain Markovian jump linear systems with time-delays which are time-varying and depend on the system mode. The parameter uncertainties are time-varying norm-bounded. The aim of this problem is to design a Markovian jump linear filter that ensures robust exponential mean-square stability of the filtering error system and a prescribed L/sub 2/- induced gain from the noise signals to the estimation error, for all admissible uncertainties. A sufficient condition for the solvability of this problem is obtained. The desired filter can be constructed by solving a set of linear matrix inequalities. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.

[1]  E. Boukas,et al.  Robust Stability and Stabilizability of Markov Jump Linear Uncertain Systems with Mode-Dependent Time Delays , 2001, ACC.

[2]  E. Boukas,et al.  Robust stability and stabilizability of Markov jump linear uncertain systems with mode-dependent time delays , 2001 .

[3]  James Lam,et al.  Robust Control of Uncertain Markovian Jump Systems with Time-Delay , 2000 .

[4]  Jong Hae Kim,et al.  Hinfinity state feedback control for generalized continuous/discrete time-delay system , 1999, Autom..

[5]  James Lam,et al.  Robust H∞ control of uncertain Markovian jump systems with time-delay , 2000, IEEE Trans. Autom. Control..

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

[7]  V. Dragan,et al.  Stability and robust stabilization to linear stochastic systems described by differential equations with markovian jumping and multiplicative white noise , 2002 .

[8]  Lihua Xie,et al.  H ∞ filtering for a class of uncertain nonlinear systems , 1993 .

[9]  K. Loparo,et al.  Stochastic stability properties of jump linear systems , 1992 .

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

[11]  Shengyuan Xu,et al.  Robust H ∞ filtering for a class of non-linear systems with state delay and parameter uncertainty , 2002 .

[12]  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..

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

[14]  Konrad Reif,et al.  The extended Kalman filter as an exponential observer for nonlinear systems , 1999, IEEE Trans. Signal Process..

[15]  Mark H. Davis.  Markov Models and Optimization , 1995 .

[16]  H. Unbehauen,et al.  Robust H∞ observer design of linear time-delay systems with parametric uncertainty , 2001 .

[17]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[18]  Zikuan Liu,et al.  Robust H∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays , 2001, IEEE Trans. Autom. Control..