On designing fault detection filter for discrete-time nonlinear Markovian jump systems with missing measurements

This paper deals with the problem of fault detection filter (FDF) design for a class of discrete-time nonlinear Markovian jump systems with missing measurements. The nonlinearity is assumed to satisfy global Lipschitz conditions. An observer-based FDF is employed as a residual generator, and then the problem is formulated into a stochastic H_∞ filtering frame. Sufficient existence conditions of the H_∞-FDF are given in terms of matrix inequalities for two cases. One is the complete known transition probabilities case while the other is the partially known transition probabilities case. Moreover, the solutions to the parameter matrices are obtained by solving a set of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the effectiveness of the proposed approach.