<italic>H</italic>_ Index for Linear Time-Varying Markov Jump Stochastic Systems and Its Application to Fault Detection

Abstract

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 time-varying stochastic systems, two necessary and sufficient conditions for the finite horizon H _ index larger than a given prescribed level $\beta > 0$ 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.