Mixed filter design for nonlinear singular Markovian jump systems with time-varying delays based on a dissipativity performance index

This paper deals with the problem of dissipative filtering for a class of nonlinear singular Markovian Jump systems (SMJSs) with time-varying delays. Our consideration is centered on the design of a mixed filter that can contain both mode-dependent and mode-independent filters in a unified framework. By using a delay-decomposition approach and constructing a mode-dependent stochastic Lyapunov-Krasovskii functional, sufficient delay-dependent conditions are derived in terms of linear matrix inequalities, which guarantee the considered nonlinear SMJSs to be stochastically admissible with a dissipativity performance . Based on the conditions, the existence conditions and parameters of the desired filter are obtained. Two numerical examples are given to illustrate the reduced conservatism and the effectiveness of the proposed methods.