On mode-dependent H∞ filtering for network-based discrete-time systems

This paper is devoted to the H"~ filtering problem for network-based discrete-time systems subject to network communication constraints. The objective is to design a network-based full-order or reduced-order filter, such that the resulting filtering error system is mean-square stable, while a prescribed H"~ disturbance attenuation levels is satisfied. A Markov chain is used to describe the network-induced delays. Then, a mode-dependent linear filter is considered, whose parameters are scheduled by the network-induced delays. By converting the partially unknown transition probability matrix to be a known convex description, and using the slack matrix approach, a new less conservative mode-dependent sufficient condition for the existence of the desired filter is derived to guarantee that the filtering error system is stochastically stable while satisfying a given H"~ performance. Based on this condition, the filter design method is proposed, and by solving some convex linear matrix inequalities, the explicit of the desired filer gain matrices is also given. Finally, a practical example is included to illustrate the effectiveness of the proposed method.

[1]  Hui Zhang,et al.  Robust energy-to-peak filtering for networked systems with time-varying delays and randomly missing data , 2010 .

[2]  Qing-Long Han,et al.  Network-Based Filtering for Discrete-Time Systems , 2012 .

[3]  Peng Shi,et al.  Central Suboptimal H∞ Filter Design for Linear Time-Varying Systems with State or Measurement Delay , 2009, Circuits Syst. Signal Process..

[4]  Yang Shi,et al.  Improved robust energy-to-peak filtering for uncertain linear systems , 2010, Signal Process..

[5]  Xiao Fan Wang,et al.  Decentralized Adaptive Pinning Control for Cluster Synchronization of Complex Dynamical Networks , 2013, IEEE Transactions on Cybernetics.

[6]  Yongduan Song,et al.  ${\cal H}_{\infty}$ Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Sirish L. Shah,et al.  Optimal Hinfinity filtering in networked control systems with multiple packet dropouts , 2008, Syst. Control. Lett..

[8]  Hui Zhang,et al.  Delay-Dependent Stabilization of Discrete-Time Systems With Time-Varying Delay via Switching Technique , 2012 .

[9]  Luca Schenato,et al.  Optimal Estimation in Networked Control Systems Subject to Random Delay and Packet Drop , 2008, IEEE Transactions on Automatic Control.

[10]  Aryan Saadat Mehr,et al.  On ${\cal H}_{\infty }$ Filtering for Discrete-Time Takagi–Sugeno Fuzzy Systems , 2012, IEEE Transactions on Fuzzy Systems.

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

[12]  Ligang Wu,et al.  A New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Time-Varying Delay Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Tongwen Chen,et al.  A new method for stabilization of networked control systems with random delays , 2005 .

[14]  Alim P. C. Gonçalves,et al.  Filtering of discrete‐time Markov jump linear systems with uncertain transition probabilities , 2011 .

[15]  Yang Shi,et al.  Output Feedback Stabilization of Networked Control Systems With Random Delays Modeled by Markov Chains , 2009, IEEE Transactions on Automatic Control.

[16]  Dong Yue,et al.  Robust H/sub /spl infin// filter design of uncertain descriptor systems with discrete and distributed delays , 2004, IEEE Transactions on Signal Processing.

[17]  Hui Zhang,et al.  Robust FIR equalization for time-varying communication channels with intermittent observations via an LMI approach , 2011, Signal Process..

[18]  Yuanqing Xia,et al.  Parameter-dependent robust H∞ filtering for uncertain discrete-time systems , 2009, Autom..

[19]  Yongduan Song,et al.  A Novel Approach to Filter Design for T–S Fuzzy Discrete-Time Systems With Time-Varying Delay , 2012, IEEE Transactions on Fuzzy Systems.

[20]  Karolos M. Grigoriadis,et al.  Delay-Dependent H ∞ Filtering for State-delayed LPV Systems , 2005 .

[21]  Nandit Soparkar,et al.  Trading computation for bandwidth: reducing communication in distributed control systems using state estimators , 2002, IEEE Trans. Control. Syst. Technol..

[22]  Quan Quan,et al.  FILTERED REPETITIVE CONTROL OF ROBOT MANIPULATORS , 2011 .

[23]  Guo-Ping Liu,et al.  Filtering for Discrete-Time Networked Nonlinear Systems With Mixed Random Delays and Packet Dropouts , 2011, IEEE Transactions on Automatic Control.

[24]  James Lam,et al.  Mixed H2/H∞ Filtering for Continuous-Time Polytopic Systems: A Parameter-Dependent Approach , 2005 .

[25]  Andrey V. Savkin,et al.  The problem of state estimation via asynchronous communication channels with irregular transmission times , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[26]  Wei Xing Zheng,et al.  H∞ filter design for nonlinear networked control systems with uncertain packet-loss probability , 2012, Signal Process..

[27]  Zidong Wang,et al.  H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities , 2008, Autom..

[28]  Huiping Li,et al.  Robust H∞ filtering for nonlinear stochastic systems with uncertainties and Markov delays , 2012, Autom..

[29]  Sirish L. Shah,et al.  Optimal H 1 filtering in networked control systems with multiple packet dropouts I , 2008 .

[30]  B. Marx,et al.  Hα-filtering and state feedback control for discrete-time switched descriptor systems , 2009 .

[31]  Jianbin Qiu,et al.  Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework , 2011, IEEE Transactions on Fuzzy Systems.

[32]  Choon Ki Ahn,et al.  L 2 - L ∞ filtering for time-delayed switched hopfield neural networks , 2011 .

[33]  Qing-Long Han,et al.  Network-Based $H_{\infty}$ Filtering for Discrete-Time Systems , 2012, IEEE Transactions on Signal Processing.

[34]  P. Shi.  Filtering on sampled-data systems with parametric uncertainty , 1998, IEEE Trans. Autom. Control..

[35]  Subhrakanti Dey,et al.  Stability of Kalman filtering with Markovian packet losses , 2007, Autom..

[36]  Michael V. Basin,et al.  Central suboptimal H ∞ filter design for linear time-varying systems with state and measurement delays , 2010, Int. J. Syst. Sci..

[37]  Hui Zhang,et al.  Robust ℋ︁∞ PID control for multivariable networked control systems with disturbance/noise attenuation , 2012 .

[38]  Qing-Long Han,et al.  Robust Hinfinity filtering for a class of uncertain linear systems with time-varying delay , 2008, Autom..

[39]  Yongduan Song,et al.  A Novel Control Design on Discrete-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delays , 2013, IEEE Transactions on Fuzzy Systems.

[40]  Oliver Sawodny,et al.  Using a Kalman filter and a Pade approximation to estimate random time delays in a networked feedback control system , 2010 .

[41]  Huijun Gao,et al.  Title H ∞ fuzzy filtering of nonlinear systems with intermittentmeasurements , 2009 .

[42]  Hui Zhang,et al.  Robust weighted H∞ filtering for networked systems with intermittent measurements of multiple sensors , 2011 .

[43]  Javad Mohammadpour,et al.  Delay-dependent Hinfinity filtering for time-delayed LPV systems , 2008, Syst. Control. Lett..

[44]  James Lam,et al.  New approach to mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems , 2005, IEEE Transactions on Signal Processing.

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

[46]  Hui Zhang,et al.  Robust equalisation for inter symbol interference communication channels , 2012, IET Signal Process..

[47]  Bo Yu,et al.  Robust mixed H2/H∞ control of networked control systems with random time delays in both forward and backward communication links , 2011, Autom..

[48]  Huijun Gao,et al.  Network-based feedback control for systems with mixed delays based on quantization and dropout compensation , 2011, Autom..

[49]  Guang-Hong Yang,et al.  Non-fragile fuzzy H∞ filter design for nonlinear continuous-time systems with D stability constraints , 2012, Signal Process..

[50]  C. Ahn,et al.  FILTERING FOR TIME-DELAYED SWITCHED HOPFIELD NEURAL NETWORKS , 2011 .

[51]  Hui Zhang,et al.  Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems , 2011, IEEE Transactions on Industrial Electronics.