H2 filter design for discrete‐time Markov jump linear systems with partly unknown transition probabilities

SUMMARY The H2 filter design problem for discrete-time Markov jump linear systems with partly unknown transition probabilities is addressed in this paper. The so-called partly unknown transition probabilities cover two cases: one is that some unknown elements have known lower and upper bounds, the other is that some unknown elements have no information available. By employing Finsler's lemma and linear matrix inequality (LMI) technique, sufficient conditions are developed in the LMI setting to design an H2 filter such that the filtering error system is mean-square stable and at the same time satisfies a prescribed H2 performance index. Numerical examples are presented to illustrate the effectiveness of the developed theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.

[1]  Alim P. C. Gonçalves,et al.  ℋ 2 filtering of discrete-time Markov jump linear systems through linear matrix inequalities , 2008, Int. J. Control.

[2]  Lixian Zhang,et al.  Discrete-time Markovian jump linear systems with partly unknown transition probabilities: H∞ filtering problem , 2008, 2008 American Control Conference.

[3]  Yuguang Fang,et al.  Stabilization of continuous-time jump linear systems , 2002, IEEE Trans. Autom. Control..

[4]  T. Chai,et al.  A robust fault detection filtering for stochastic distribution systems via descriptor estimator and parametric gain design , 2007 .

[5]  M. Fragoso,et al.  Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters , 1993 .

[6]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[7]  A. Hassibi,et al.  Control with random communication delays via a discrete-time jump system approach , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[8]  Hong Wang,et al.  Discrete-time proportional and integral observer and observer-based controller for systems both with unknown input and output disturbances , 2007 .

[9]  L. Ghaoui,et al.  Robust state-feedback stabilization of jump linear systems , 1996 .

[10]  Alexandre Trofino,et al.  Mode-Independent ${\cal H}_{\infty}$ Filters for Markovian Jump Linear Systems , 2006, IEEE Transactions on Automatic Control.

[11]  J. Geromel,et al.  A Convex Programming Approach to the H2-Control of Discrete-Time Markovian Jump Linear Systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[12]  James Lam,et al.  Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities , 2008, IEEE Transactions on Automatic Control.

[13]  J. Geromel,et al.  A new discrete-time robust stability condition , 1999 .

[14]  José Claudio Geromel,et al.  Output feedback control of Markov jump linear systems in continuous-time , 2000, IEEE Trans. Autom. Control..

[15]  Peng Shi,et al.  Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems , 2006, Autom..

[16]  Bing Chen,et al.  Delay-dependent stability analysis and controller synthesis for Markovian jump systems with state and input delays , 2009, Inf. Sci..

[17]  Zhiwei Gao,et al.  Reliable Observer-Based Control Against Sensor Failures for Systems With Time Delays in Both State and Input , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[18]  Alim P. C. Gonçalves,et al.  The H2-control for jump linear systems: cluster observations of the Markov state , 2002, Autom..

[19]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[20]  Guang-Hong Yang,et al.  Robust H2 control of continuous-time Markov jump linear systems , 2008, Autom..

[21]  Johan Nilsson,et al.  Real-Time Control Systems with Delays , 1998 .

[22]  E. Boukas,et al.  H∞ control for discrete‐time Markovian jump linear systems with partly unknown transition probabilities , 2009 .

[23]  Huijun Gao,et al.  New results on stabilization of Markovian jump systems with time delay , 2009, Autom..