H ∞ filtering for systems with time-varying delay satisfying a certain stochastic characteristic

This study proposes a class of H ∞ filter design for linear time-delay system. The time delay considered here is assumed to be satisfying a certain stochastic characteristic. Corresponding to the probability of the delay taking value in different intervals, a stochastic variable satisfying Bernoulli random binary distribution is introduced and a new system model is established by employing the information of the probability distribution. Then new criteria is derived for the filtering-error systems, which can lead to much less conservative analysis results. It should be noted that the solvability of the obtained criteria depend not only on the size of the delay, but also the probability distribution of it. At last, numerical examples are given to demonstrate the effectiveness and the merit of the proposed method.

[1]  Shengyuan Xu,et al.  Technical communique: New results on delay-dependent robust H∞ control for systems with time-varying delays , 2006 .

[2]  James Lam,et al.  Robust energy-to-peak filter design for stochastic time-delay systems , 2006, Syst. Control. Lett..

[3]  Jinliang Liu,et al.  H∞ filtering for Markovian jump systems with time-varying delays , 2010, 2010 Chinese Control and Decision Conference.

[4]  Fuwen Yang,et al.  Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements , 2006, IEEE Transactions on Signal Processing.

[5]  Dong Yue,et al.  STATE FEEDBACK CONTROLLER DESIGN OF NETWORKED CONTROL SYSTEMS WITH PARAMETER UNCERTAINTY AND STATE‐DELAY , 2006 .

[6]  Emilia Fridman,et al.  A descriptor system approach to H∞ control of linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[7]  Daniel W. C. Ho,et al.  Robust filtering under randomly varying sensor delay with variance constraints , 2003, IEEE Transactions on Circuits and Systems II: Express Briefs.

[8]  Riccardo Bettati,et al.  Providing statistical delay guarantees in wireless networks , 2004, 24th International Conference on Distributed Computing Systems, 2004. Proceedings..

[9]  Qing-Long Han,et al.  On Hinfinity control for linear systems with interval time-varying delay , 2005, Autom..

[10]  Fuwen Yang,et al.  H∞ control for networked systems with random communication delays , 2006, IEEE Trans. Autom. Control..

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

[12]  Xi Li,et al.  Delay-dependent robust H control of uncertain linear state-delayed systems , 1999, Autom..

[13]  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).

[14]  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..

[15]  Dong Yue,et al.  State feedback controller design of networked control systems , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

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

[18]  Xiefu Jiang,et al.  Delay-dependent H/sub /spl infin// filter design for linear systems with interval time-varying delay , 2007 .

[19]  Dong Yue,et al.  Delay‐distribution‐dependent robust stability of uncertain systems with time‐varying delay , 2009 .

[20]  C. Peng,et al.  Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay , 2008 .

[21]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

[22]  Wook Hyun Kwon,et al.  Delay-dependent robust Hinfinity control for uncertain systems with a state-delay , 2004, Autom..

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

[24]  Emilia Fridman,et al.  Robust H∞ control of distributed delay systems with application to combustion control , 2001, IEEE Trans. Autom. Control..

[25]  Huijun Gao,et al.  ${\cal H}_{\infty}$ Estimation for Uncertain Systems With Limited Communication Capacity , 2007, IEEE Transactions on Automatic Control.

[26]  Qing-Long Han,et al.  A less conservative method for designing H∞ filters for linear time‐delay systems , 2009 .

[27]  M. Grimble,et al.  A New Approach to the H ∞ Design of Optimal Digital Linear Filters , 1989 .

[28]  Dong Yue,et al.  Network-based robust H ∞ control of systemswith uncertainty , 2005 .

[29]  Yong He,et al.  Delay-dependent stabilization of linear systems with time-varying state and input delays , 2005, Autom..