Fuzzy model-based robust H∞ filtering for a class of nonlinear nonhomogeneous Markov jump systems

Abstract

This paper studies the problem of robust fuzzy H∞ filtering for a class of uncertain nonlinear discrete-time Markov jump systems with nonhomogeneous jump transition probabilities. The Takagi and Sugeno fuzzy model is employed to represent such nonlinear nonhomogeneous Markov jump system with norm-bounded parameter uncertainties. By Lyapunov function approach, under the designed mode-dependent and variation-dependent fuzzy filter which includes the membership functions, a sufficient condition is presented to ensure that the filtering error dynamic system is stochastically stable and has a prescribed H∞ performance index. An example is given to demonstrate the effectiveness and advantages of the proposed techniques.