$H_-$ Index for Linear Markov Jump Continous Stochastic Systems

Abstract

This paper focuses on the problem of $H_-$ index for linear Markov jump stochastic systems. Firstly, a set of finite horizon backward generalized differential Riccati equations (GDREs) and a set of matrix inequalities are introduced. Then, based on the introduced backward GDREs and matrix inequalities, for nominal Markov jump linear time-varying stochastic systems, two necessary and sufficient conditions for thefinite horizon $H_-$ index largerthan a given prescribed level $beta>0$ are given. Secondly, considering Markov jump linear uncertain stochastic systems, we obtain two results about finite horizon $H_-$ index.