Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties

This paper investigates the problem of robust reliable dissipative filtering for a class of Markovian jump nonlinear systems with uncertainties and time-varying transition probability matrix described by a polytope. Our main attention is focused on the design of a reliable dissipative filter performance for the filtering error system such that the resulting error system is stochastically stable and strictly Q,S,R dissipative. By introducing a novel augmented Lyapunov-Krasovskii functional, a new set of sufficient conditions is obtained for the existence of reliable dissipative filter design in terms of linear matrix inequalities LMIs. More precisely, a sufficient LMI condition is derived for reliable dissipative filtering that unifies the conditions for filtering with passivity and H∞ performances. Moreover, the filter gains are characterized in terms of solution to a set of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness and potential of the proposed design technique. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  P. SELVARAJ,et al.  Dissipative sampled-data control of uncertain nonlinear systems with time-varying delays , 2016, Complex..

[2]  James Lam,et al.  Stability and Stabilization for Markovian Jump Time-Delay Systems With Partially Unknown Transition Rates , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  Renquan Lu,et al.  H∞ filtering for singular systems with communication delays , 2010, Signal Process..

[4]  Qingling Zhang,et al.  Stochastic stability and stabilization of discrete‐time singular Markovian jump systems with partially unknown transition probabilities , 2015 .

[5]  Ju H. Park,et al.  Reliable mixed passive and ℋ∞ filtering for semi‐Markov jump systems with randomly occurring uncertainties and sensor failures , 2015 .

[6]  Fei Liu,et al.  Filtering for discrete-time nonhomogeneous Markov jump systems with uncertainties , 2014, Inf. Sci..

[7]  Peng Shi,et al.  Asynchronous I2-I∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014, Autom..

[8]  R. P. Marques,et al.  Discrete-Time Markov Jump Linear Systems , 2004, IEEE Transactions on Automatic Control.

[9]  Dong Yue,et al.  Robust control for Markovian jump systems with partially known transition probabilities and nonlinearities , 2013, J. Frankl. Inst..

[10]  Renquan Lu,et al.  Passivity-based non-fragile control for Markovian jump systems with aperiodic sampling , 2015, Syst. Control. Lett..

[11]  Renquan Lu,et al.  Mode-dependent quantised H∞ filtering for Markovian jump singular system , 2015, Int. J. Syst. Sci..

[12]  Shengyuan Xu,et al.  Filtering of Markovian Jump Delay Systems Based on a New Performance Index , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Gang Feng,et al.  Reliable dissipative control for stochastic impulsive systems , 2008, Autom..

[14]  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.

[15]  Zhengzhi Han,et al.  Robust stability and stabilization of linear stochastic systems with Markovian switching and uncertain transition rates , 2014 .

[16]  Ju H. Park,et al.  Robust mixed H∞ and passive filtering for networked Markov jump systems with impulses , 2014, Signal Process..

[17]  Ju H. Park,et al.  Extended Dissipative Analysis for Neural Networks With Time-Varying Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Guang-Hong Yang,et al.  Fault detection for a class of nonlinear stochastic systems with Markovian switching and mixed time-delays , 2014, Int. J. Syst. Sci..

[19]  Hongsheng Xi,et al.  Markovian-Based Fault-Tolerant Control for Wheeled Mobile Manipulators , 2012, IEEE Transactions on Control Systems Technology.

[20]  Chenghui Zhang,et al.  Stability and robust stabilisation for a class of non-linear uncertain discrete-time descriptor Markov jump systems , 2012 .

[21]  Yu Zhang.  Stability of discrete-time Markovian jump delay systems with delayed impulses and partly unknown transition probabilities , 2014 .

[22]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[23]  Li Sheng,et al.  Dissipative control for Markov jump non-linear stochastic systems based on T–S fuzzy model , 2014, Int. J. Syst. Sci..

[24]  Peng Shi,et al.  Reliable Mixed $H_\infty $ and Passivity-Based Control for Fuzzy Markovian Switching Systems With Probabilistic Time Delays and Actuator Failures , 2015, IEEE Transactions on Cybernetics.

[25]  P. Moylan,et al.  Dissipative Dynamical Systems: Basic Input-Output and State Properties , 1980 .

[26]  Fei Liu,et al.  Robust control on saturated Markov jump systems with missing information , 2014, Inf. Sci..

[27]  Hong Zhu,et al.  Finite-time H∞ estimation for discrete-time Markov jump systems with time-varying transition probabilities subject to average dwell time switching , 2015, Commun. Nonlinear Sci. Numer. Simul..

[28]  Ju H. Park,et al.  Robust reliable dissipative filtering for networked control systems with sensor failure , 2014, IET Signal Process..

[29]  Qi Huang,et al.  Globally exponential stability and stabilization of interconnected Markovian jump system with mode-dependent delays , 2016, Int. J. Syst. Sci..

[30]  Rathinasamy Sakthivel,et al.  Dissipative reliable controller design for uncertain systems and its application , 2015, Appl. Math. Comput..

[31]  Hongye Su,et al.  Optimal Estimation in UDP-Like Networked Control Systems With Intermittent Inputs: Stability Analysis and Suboptimal Filter Design , 2016, IEEE Transactions on Automatic Control.