Dissipativity-based filtering of nonlinear periodic Markovian jump systems: The discrete-time case

This paper is concerned with the problem of dissipative filtering for discrete-time periodic Markovian jump systems with bounded nonlinearity. It is assumed that the data measurements from the plant to the filter are subject to randomly occurred packet dropouts satisfying Bernoulli distribution. The purpose of this paper is to design a filter such that the filtering error system is stochastically stable and strictly (Q,S,R)(Q,S,R)-dissipative. To eliminate the cross coupling between the Lyapunov matrix and system matrices, some slack matrix variables are introduced. Based on a mode-dependent and basis-dependent Lyapunov function, a sufficient condition of the desired dissipative filter in terms of linear matrix inequalities (LMIs) for discrete-time Periodic Markovian Jump Systems with bounded nonlinearity is derived. Finally, a numerical example is exploited to demonstrate the effectiveness of the proposed filter design method.