H∞Filtering for Discrete Markov Jump Singular Systems with Mode-Dependent Time Delay Based on T-S Fuzzy Model

Cheng Gong,Yi Zeng

doi:10.1155/2014/618046

Abstract

This paper investigates theH∞filtering problem of discrete singular Markov jump systems (SMJSs) with mode-dependent time delay based on T-S fuzzy model. First, by Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition onH∞-disturbance attenuation is presented, in which both stability and prescribedH∞performance are required to be achieved for the filtering-error systems. Then, based on the condition, the delay-dependentH∞filter design scheme for SMJSs with mode-dependent time delay based on T-S fuzzy model is developed in term of linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of the result.

Highlights

Some efforts on filtering and control problem have been put on the Markov jump linear systems with Markovian jump time delays [1,2,3,4,5,6,7]
The transition of the jumping parameters in the systems is governed by a finite state Markov process. [2] addressed the problems of delay-dependent robust H∞ control and filtering for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays
The l2-l∞ fuzzy control problem was considered for nonlinear stochastic Markov jump systems with neutral time-delays in [5]

Summary

Introduction

Some efforts on filtering and control problem have been put on the Markov jump linear systems with Markovian jump time delays [1,2,3,4,5,6,7]. [2] addressed the problems of delay-dependent robust H∞ control and filtering for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays. The robust H∞ filtering problem for mode-dependent time-delay discrete Markov jump singular systems with parameter uncertainties is discussed in [3]. Reference [21] dealt with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory neural networks with timevarying interval delays and Markovian jumping parameters by T-S fuzzy model. Many references [29,30,31] discussed the control problems for SMJSs. to the best of our knowledge, the H∞ filtering problem of discrete SMJSs with mode-dependent time delay based on T-S fuzzy model has not been addressed, which is the focus of this paper. If not explicitly stated, are assumed to have compatible dimensions for algebraic operations

System Descriptions and Preliminaries

Main Results

Example

Conclusion