l2-l∞ filter design for discrete-time singular Markovian jump systems with time-varying delays

The problem of l"2-l"~ filter design for discrete-time singular systems with Markovian jump and time-varying delays is investigated in this paper. By using the delay partitioning technique, a delay-dependent condition is established to guarantee the filtering error systems to be stochastically admissible and achieve a prescribed l"2-l"~ performance index. Based on the derived condition, the full-order and reduced-order filters with mode-independent characterization are designed in a unified framework. The corresponding filter parameters can be obtained by solving a set of linear matrix inequalities. The reported results not only depend upon the delay, but also depend upon the partitioning, which aims at reducing the conservatism. Two numerical examples are provided to illustrate the effectiveness of the proposed methods.

[1]  Jong-Hae Kim,et al.  Delay-dependent robust Hinfinity filtering for uncertain discrete-time singular systems with interval time-varying delay , 2010, Autom..

[2]  Shengyuan Xu,et al.  Robust admissibility of time-varying singular systems with commensurate time delays , 2009, Autom..

[3]  James Lam,et al.  Robust state estimation for stochastic genetic regulatory networks , 2010, Int. J. Syst. Sci..

[4]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[5]  Bing Chen,et al.  New results on delay-dependent robust stability of uncertain time delay systems , 2010, Int. J. Syst. Sci..

[6]  H. Su,et al.  H∞ filtering for singular systems with time‐varying delay , 2010 .

[7]  Yurong Liu,et al.  A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances , 2010, Autom..

[8]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[9]  Hongye Su,et al.  Delay-dependent H∞ filtering for singular Markovian jump time-delay systems , 2010, Signal Process..

[10]  Shengyuan Xu,et al.  Robust Control and Filtering of Singular Systems , 2006 .

[11]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[12]  Shengyuan Xu,et al.  Robust H∞ control for uncertain fuzzy systems with distributed delays via output feedback controllers , 2008, Inf. Sci..

[13]  P. Shi.  On H∞ Control Design for Singular Continuous-Time Delay Systems with Parametric Uncertainties , 2004 .

[14]  Zidong Wang,et al.  Robust passivity and passification of stochastic fuzzy time-delay systems , 2010, Inf. Sci..

[15]  Wei Xing Zheng,et al.  Passivity-based sliding mode control of uncertain singular time-delay systems , 2009, Autom..

[16]  Huijun Gao,et al.  New results on H∞ filtering for fuzzy systems with interval time-varying delays , 2011, Inf. Sci..

[17]  Xiaodong Liu,et al.  New results on delay-dependent robust stability criteria of uncertain fuzzy systems with state and input delays , 2009, Inf. Sci..

[18]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[19]  Donghua Zhou,et al.  Robust $H_{\infty}$ Filtering for Time-Delay Systems With Probabilistic Sensor Faults , 2009, IEEE Signal Processing Letters.

[20]  Dimitri Peaucelle,et al.  Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation , 2007, Autom..

[21]  Vasile Dragan,et al.  Control of singularly perturbed systems with Markovian jump parameters: an Hinfinity approach , 1999, Autom..

[22]  Fuchun Sun,et al.  Design of Hinfinity filter for Markov jumping linear systems with non-accessible mode information , 2008, Autom..

[23]  J. Lam,et al.  Delay-dependent robust H∞ control for uncertain systems with time-varying delays , 1998 .

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

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

[26]  Guo-Ping Liu,et al.  Output Feedback Stabilization for a Discrete-Time System With a Time-Varying Delay , 2008, IEEE Transactions on Automatic Control.

[27]  Daniel W. C. Ho,et al.  Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements , 2009, Autom..

[28]  Chen Peng,et al.  Delay-dependent robust H∞ control for uncertain systems with time-varying delay , 2009, Inf. Sci..

[29]  E. Boukas,et al.  Robust H∞ filtering for uncertain discrete Markov jump singular systems with mode-dependent time delay , 2009 .

[30]  Huijun Gao,et al.  Stability analysis for continuous systems with two additive time-varying delay components , 2007, Syst. Control. Lett..

[31]  Zidong Wang,et al.  A delay-dependent approach to H ∞ filtering for stochastic delayed jumping systems with sensor non-linearities , 2007, Int. J. Control.

[32]  Yuanqing Xia,et al.  Stability and stabilization of continuous-time singular hybrid systems , 2009, Autom..

[33]  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.

[34]  Huijun Gao,et al.  Input-Delayed Control of Uncertain Seat Suspension Systems With Human-Body Model , 2010, IEEE Transactions on Control Systems Technology.

[35]  Bing Chen,et al.  Direct adaptive fuzzy control for nonlinear systems with time-varying delays , 2010, Inf. Sci..

[36]  Peng Shi,et al.  Asymptotic H∞ control of singularly perturbed systems with parametric uncertainties , 1999, IEEE Trans. Autom. Control..

[37]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[38]  James Lam,et al.  Further Results on Exponential Estimates of Markovian Jump Systems With Mode-Dependent Time-Varying Delays , 2011, IEEE Transactions on Automatic Control.

[39]  H. Su,et al.  H∞ filtering for singular Markovian jump systems with time delay , 2010 .