Fault Detection Filter Design for Markovian Jump Singular Systems

Abstract

This chapter investigates the fault detection filter design problem for discrete-time Markovian jump singular systems with intermittent measurements. The data missing phenomena is modeled by a Bernoulli distributed stochastic variable. With the introduction of new definitions of stochastic Markovian jump stability and stochastic admissibility for such systems, a new necessary and sufficient condition for Markovian jump singular systems to be stochastically admissible is derived in terms of strict linear matrix inequalities (LMIs). Subsequently, the existence of the $\mathcal {H}_{\infty }$ fault detection filter such that the residual system is stochastically admissible and meets certain performance requirements is solved. Moreover, the explicit expression of the desired filter parameters is also provided. It is shown that the desired $\mathcal {H}_{\infty }$ fault detection filter can be obtained by solving a convex optimization problem readily with standard numerical software.