Robust H ∞ Filtering for a Class of Nonlinear Discrete-Time Markovian Jump Systems

Abstract

This paper considers the problem of the robust H∞ filtering for a class of nonlinear discrete-time Markovian jump systems with real time-varying norm-bounded parameter uncertainty. For each mode, the nonlinearity is assumed to satisfy the global Lipschitz conditions and appears in both the state and measured output equations. The problem that we address is the design of a nonlinear filter which ensures robust stochastic stability and a prescribed H∞ performance level of the filtering error system for all admissible uncertainties. A sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities; an explicit expression of a desired nonlinear H∞ filter is also given. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.