H∞ filtering for Markovian jump systems with time-varying delays

This paper proposes a class of H∞ filter design for Markovian jump systems with time-varying delays. Firstly, exploiting a new Lyapunov function and using the convexity property of the matrix inequality, new criteria are derived for the H∞ performance analysis of the filtering-error systems,which can lead to much less conservative analysis results. Secondly, based on the obtained conditions, the gain of filter can be obtained in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the effectiveness and the merit of the proposed method.

[1]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

[2]  El-Kébir Boukas,et al.  Delay-dependent robust stability and H/sub /spl infin// control of jump linear systems with time-delay , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[3]  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..

[4]  Z. Liu,et al.  Delay-dependent robust stability and H8 control of jump linear systems , 2001 .

[5]  Xuerong Mao,et al.  Exponential stability of stochastic delay interval systems with Markovian switching , 2002, IEEE Trans. Autom. Control..

[6]  Zidong Wang,et al.  Robust filtering under randomly varying sensor delay with variance constraints , 2003, ECC.

[7]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[8]  Daniel W. C. Ho,et al.  Filtering on nonlinear time-delay stochastic systems , 2003, Autom..

[9]  James Lam,et al.  Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[10]  Dong Yue,et al.  Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching , 2005, IEEE Transactions on Automatic Control.

[11]  Engang Tian,et al.  Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay , 2006, Fuzzy Sets Syst..

[12]  P. Shi,et al.  Delay-Dependent H/spl infin/ filtering for Uncertain Time Delay Nonlinear Systems: An LMI Approach , 2006, 2006 American Control Conference.

[13]  Shaocheng Tong,et al.  Delay-dependent stability analysis and control synthesis of fuzzy dynamic systems with time delay , 2006, Fuzzy Sets Syst..

[14]  Zidong Wang,et al.  Exponential stability of delayed recurrent neural networks with Markovian jumping parameters , 2006 .

[15]  E. Boukas,et al.  Mode-dependent Hºº filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities. , 2007 .

[16]  Yong-Yan Cao,et al.  Delay‐dependent filtering design for time‐delay systems with Markovian jumping parameters , 2007 .

[17]  E. Sánchez,et al.  OPTIMAL LINEAR FILTERING FOR SYSTEMS WITH MULTIPLE STATE AND OBSERVATION DELAYS , 2007 .

[18]  Han-Xiong Li,et al.  New Approach to Delay-Dependent Stability Analysis and Stabilization for Continuous-Time Fuzzy Systems With Time-Varying Delay , 2007, IEEE Transactions on Fuzzy Systems.

[19]  Marcelo D. Fragoso,et al.  A separation principle for the H2-control of continuous-time infinite markov jump linear systems with partial observations , 2007, 2007 European Control Conference (ECC).

[20]  Qing-Long Han,et al.  Robust $H_{\infty}$ Control for Uncertain Takagi–Sugeno Fuzzy Systems With Interval Time-Varying Delay , 2007, IEEE Transactions on Fuzzy Systems.

[21]  Shengyuan Xu,et al.  Delay-Dependent $H_{\infty }$ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  J. Lam,et al.  Robust H ∞ Control and Filtering of Networked Control Systems , 2008 .

[23]  Hanyong Shao.  Delay-range-dependent robust H∞ filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters , 2008 .

[24]  James Lam,et al.  Robust H 2 control of Markovian jump systems with uncertain switching probabilities , 2009, Int. J. Syst. Sci..

[25]  Lixian Zhang,et al.  Mode-dependent Hinfinity filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[26]  Huaicheng Yan,et al.  Robust H∞ filters for Markovian jump linear systems under sampled measurements , 2009 .

[27]  Dong Yue,et al.  Delay-Distribution-Dependent Stability and Stabilization of T–S Fuzzy Systems With Probabilistic Interval Delay , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[28]  Jinliang Liu,et al.  H 8 Filtering for time‐delay systems with Markovian jumping parameters: Delay partitioning approach , 2010 .