Nonlinear filtering for state delayed systems with Markovian switching

This paper deals with the filtering problem for a general class of nonlinear time-delay systems with Markovian jumping parameters. The nonlinear time-delay stochastic systems may switch from one to the others according to the behavior of a Markov chain. The purpose of the problem addressed is to design a nonlinear full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially stable in the mean square. Both filter analysis and synthesis problems are investigated. Sufficient conditions are established for the existence of the desired exponential filters, which are expressed in terms of the solutions to a set of linear matrix inequalities (LMIs). The explicit expression of the desired filters is also provided. A simulation example is given to illustrate the design procedures and performances of the proposed method.

[1]  E. Yaz,et al.  Observer design for discrete and continuous non-linear stochastic systems , 1993 .

[2]  Keith J. Burnham,et al.  Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation , 2001, IEEE Trans. Signal Process..

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

[4]  C. Scherer.  Robust generalized H/sub 2/ control for uncertain and LPV systems with general scalings , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[5]  J. Lam,et al.  Stochastic stabilizability and H∞ control for discrete-time jump linear systems with time delay ☆ , 1999 .

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

[7]  William M. McEneaney,et al.  A Max-Plus-Based Algorithm for a Hamilton--Jacobi--Bellman Equation of Nonlinear Filtering , 2000, SIAM J. Control. Optim..

[8]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

[9]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[10]  Jerzy A. Filar,et al.  Stability analysis and controller design for a class of uncertain systems with Markovian jumping parameters , 2000 .

[11]  X. Mao.  Stability of stochastic differential equations with Markovian switching , 1999 .

[12]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[13]  T. Tarn,et al.  Observers for nonlinear stochastic systems , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[14]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

[15]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[16]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[17]  Peng Shi,et al.  Nonlinear H filtering of sampled-data systems , 2000, Autom..

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

[19]  Heinz Unbehauen,et al.  Robust Hinfinity observer design of linear state delayed systems with parametric uncertainty: the discrete-time case , 1999, Autom..

[20]  M. Mahmoud,et al.  Robust Kalman filtering for continuous time-lag systems , 1999 .

[21]  Jean-Michel Dion,et al.  Stability and robust stability of time-delay systems: A guided tour , 1998 .