Extended ℋ∞ Estimation for Two-Dimensional Markov Jump Systems under Asynchronous Switching

This paper is concerned with the problem of designing ℋ∞ filters for a class of two-dimensional (2D) Markov jump systems under asynchronous switching. The problem under consideration is primarily motivated by a realistic situation that the switching of candidate filters may have a lag to the switching of system modes. Different from conventional techniques, by a suitable augmentation, the jumping process of the error system is represented by a two-component Markov chain. Then, the extended transition probabilities are provided for the error system. A stochastic Lyapunov function approach is proposed for the design of desired filters that ensure a prescribed ℋ∞ performance for admissible asynchronous switching. Finally, a numerical example is given to illustrate the effectiveness of the developed method.

[1]  Lihua Xie,et al.  Robust filtering for 2-D discrete-time linear systems with convex-bounded parameter uncertainty , 2010, Autom..

[2]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[3]  Truong Q. Nguyen,et al.  Robust mixed generalized H/sub 2//H/sub /spl infin// filtering of 2-D nonlinear fractional transformation systems , 2005, IEEE Transactions on Signal Processing.

[4]  Chen Peng,et al.  Brief paper: reliable control for networked control systems with probabilistic sensors and actuators faults , 2010 .

[5]  Ye Zhao,et al.  Asynchronous Filtering of Discrete-Time Switched Linear Systems With Average Dwell Time , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Ligang Wu,et al.  Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems , 2012, Autom..

[7]  Zidong Wang,et al.  Mathematical Problems for Complex Networks , 2012 .

[8]  Y. Zhang,et al.  Brief paper: Delay-range-dependent H ∞ filtering for two-dimensional markovian jump systems with interval delays , 2011 .

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

[10]  Yun Zou,et al.  Robust H∞ filtering for uncertain two-dimensional discrete systems with state-varying delays , 2010 .

[11]  Lihua Xie,et al.  H∞ deconvolution filtering of 2-d digital systems , 2002, IEEE Trans. Signal Process..

[12]  胡超,et al.  Asynchronous H∞ filtering for a class of two-dimensional markov jump systems , 2012 .

[13]  M. Sebek,et al.  Polynomial solution of 2D Kalman-Bucy filtering problem , 1992 .

[14]  Huijun Gao,et al.  Stabilization and H∞ control of two-dimensional Markovian jump systems , 2004, IMA J. Math. Control. Inf..

[15]  Dong Yue,et al.  T–S Fuzzy Model-Based Robust Stabilization for Networked Control Systems With Probabilistic Sensor and Actuator Failure , 2011, IEEE Transactions on Fuzzy Systems.

[16]  Wojciech Paszke,et al.  Robust H/sub /spl infin// filtering for Uncertain2-D continuous systems , 2005, IEEE Transactions on Signal Processing.

[17]  JOHN w. WOODS,et al.  Kalman filtering in two dimensions , 1977, IEEE Trans. Inf. Theory.

[18]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

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

[20]  Huijun Gao,et al.  ℋ︁∞ and l2–l∞ filtering for two‐dimensional linear parameter‐varying systems , 2007 .

[21]  Li Xu,et al.  Delay-dependent robust stability and stabilisation of uncertain two-dimensional discrete systems with time-varying delays , 2010 .

[22]  Qiusheng He,et al.  Asynchronous H ∞ filtering for a class of two-dimensional markov jump systems [Brief Paper] , 2012 .

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

[24]  Yugang Niu,et al.  Stabilization of Markovian jump linear system over networks with random communication delay , 2009, Autom..