Filtering-based fault detection for a class of piecewise homogeneous Markov jump systems

The fault detection problem of a class of piecewise homogeneous Markov jump systems is proposed in this study. The main objective of this study is to design a fault detection filter, which ensures that the error system is stochastically stable with an H_∞ disturbance attenuation. Based on a stochastic Lyapunov-Krasovskii functional, a delay-dependent bounded real lemma for the error system is established in terms of linear matrix inequalities. Moreover, the solvability condition of fault detection filter is given. The validity of the proposed results is illustrated via a numerical example.