H∞ fault detection filter design for discrete-time nonlinear Markovian jump systems with missing measurements

Abstract

Fault detection filter (FDF) design problem for a class of discrete-time nonlinear Markovian jump systems subject to unreliable communication channel is addressed in this study. The considered system nonlinearity is assumed to satisfy global Lipschitz condition and the missing measurement phenomenon is modeled by Bernoulli binary distribution. By constructing an observer-based FDF as a residual generator, the fault detection issue is cast into a stochastic H∞ filtering framework. Sufficient existence conditions of the H∞-FDF are derived via matrix inequalities. Two cases for the Markovian parameters, one is completely known transition probabilities and the other is partially known transition probabilities, have been considered in the filter design procedure, respectively. Furthermore, parameter matrices of the FDF are obtained by solving a set of linear matrix inequalities. An illustrative example is addressed to show the efficacy of the proposed filter.