Design of reduced-order H∞ filter for Markovian jumping systems with time delay

This brief is concerned with the reduced-order H/sub /spl infin// filtering problem for Markovian jumping linear systems with time delay, where the jumping parameters are modeled by a discrete-time Markov process. Sufficient conditions for the existence of the reduced-order H/sub /spl infin// filter are proposed in terms of linear matrix inequalities (LMI) and a coupling nonconvex matrix rank constraint. In particular, the sufficient conditions for the existence of the zeroth-order (or static) H/sub /spl infin// filter can be expressed in terms of a set of strict LMIs. The explicit parameterization of the desired filter is also given. Finally, a numerical example is given to illustrate the proposed approach.

[1]  Craig S. Sims,et al.  Reduced-order estimation Part 1. Filtering , 1987 .

[2]  Ali Feliachi,et al.  Reduced Order Estimation , 1989, 1989 American Control Conference.

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

[4]  U. Shaked,et al.  H,-OPTIMAL ESTIMATION: A TUTORIAL , 1992 .

[5]  Tetsuya Iwasaki,et al.  All controllers for the general H∞ control problem: LMI existence conditions and state space formulas , 1994, Autom..

[6]  Lihua Xie,et al.  On robust filtering for linear systems with parameter uncertainty , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[7]  T. Başar,et al.  H/sup /spl infin// control of large scale jump linear systems via averaging and aggregation , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[8]  Karolos M. Grigoriadis,et al.  Low-order control design for LMI problems using alternating projection methods , 1996, Autom..

[9]  K. Grigoriadis,et al.  Reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[10]  W. McEneaney.  Robust/ H ∞ filtering for nonlinear systems , 1998 .

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

[12]  Peng Shi,et al.  Robust control for Markovian jumping discrete-time systems , 1999, Int. J. Syst. Sci..

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

[14]  Marcelo D. Fragoso,et al.  H ∞ filtering for Markovian jump linear systems , 2002, Int. J. Syst. Sci..

[15]  Y. Hung,et al.  Robust mixed H/sub 2//H/sub /spl infin// filtering with regional pole assignment for uncertain discrete-time systems , 2002 .

[16]  O. Costa,et al.  Robust linear filtering for discrete-time hybrid Markov linear systems , 2002 .

[17]  Shengyuan Xu,et al.  Reduced-order H∞ filtering for stochastic systems , 2002, IEEE Trans. Signal Process..

[18]  M. Fragoso,et al.  Robust ℋ︁∞ filtering for uncertain Markovian jump linear systems , 2002 .

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

[20]  Shengyuan Xu.  Robust H/sub /spl infin// filtering for a class of discrete-time uncertain nonlinear systems with state delay , 2002 .

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

[22]  Huijun Gao,et al.  Robust L/sub 2/-L/sub /spl infin// filtering for uncertain systems with multiple time-varying state delays , 2003 .