Asynchronous Filtering of Nonlinear Markov Jump Systems with Randomly Occurred Quantization via T-S Fuzzy Models

Abstract

This paper focuses on the dissipativity-based asynchronous filtering problem for a class of discrete-time Takagi–Sugeno fuzzy Markov jump systems subject to randomly occurred quantization. Considering the random fluctuations of network conditions, the randomly occurred quantization is introduced to describe the quantization phenomenon appearing in a probabilistic way. To take full advantage of the partial information of system modes for the desired system performance, we adopt the asynchronous filter in which mode transition matrix is nonhomogeneous. The mode-dependent time-varying delays are introduced, which have different bounds for different system modes. Via fuzzy-mode-dependent Lyapunov functional approach that can reduce conservatism, a sufficient condition on the existence of the asynchronous filter is derived such that the filtering error system is stochastically stable and strictly $(\mathcal{Q}, \mathcal{S},\mathcal{R})$ -dissipative. Then, the gains of the filter are obtained by solving a set of linear matrix inequalities (LMIs). An example is utilized to illustrate the validity of the developed filter design technique where the relationships among optimal dissipative performance indices, delays, quantization parameter, and the degree of asynchronous jumps are given.