H∞ Filtering for a Class of Uncertain Markov Jump Nonlinear Systems

This paper deals with the problem of robust H_∞ filtering for a class of Markov jump nonlinear systems subject to constant convex-bounded uncertain parameters. The system is described by a differential-algebraic representation, which can model the whole class of Markov jump systems with rational functions of the state and uncertain parameters, as well as some trigonometric nonlinearities. The design of mode-dependent (Markov jump) and mode-independent linear filters is considered. The proposed designs are based on the notion of exponential mean square stability together with a stochastic Lyapunov function with polynomial dependence on the system state and uncertain parameters, and are given in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the derived results