Robust Filtering for Nonlinear Nonhomogeneous Markov Jump Systems by Fuzzy Approximation Approach

This paper addresses the problem of robust fuzzy L₂ - L_∞ filtering for a class of uncertain nonlinear discrete-time Markov jump systems (MJSs) with nonhomogeneous jump processes. The Takagi-Sugeno fuzzy model is employed to represent such nonlinear nonhomogeneous MJS with norm-bounded parameter uncertainties. In order to decrease conservation, a polytope Lyapunov function which evolves as a convex function is employed, and then, 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 that it has a prescribed L₂ - L_∞ performance index. Two simulated examples are given to demonstrate the effectiveness and advantages of the proposed techniques.