H_ Index for Linear Time-Varying Markov Jump Stochastic Systems and Its Application to Fault Detection

In this paper, the H_ index for Markov jump linear time-varying stochastic systems and its application to robust H_ fault detection filter (FDF) are under consideration. First, a set of finite horizon backward generalized differential Riccati equations (GDREs) and a set of matrix inequalities are introduced. Based on the introduced backward GDREs and matrix inequalities, for nominal Markov jump linear timevarying stochastic systems, two necessary and sufficient conditions for the finite horizon H_ index larger than a given prescribed level β > 0 are given. Second, for norm uncertain Markov jump linear time-varying stochastic systems, sufficient conditions are presented in terms of matrix inequalities. As applications, two equivalent conditions for the existence of robust H_ FDF are obtained for nominal linear stochastic systems. In particular, under the case of norm uncertainties, a robust H_ FDF is designed based on the feasibility of linear matrix inequalities.