Almost Sure Stability of Switching Markov Jump Linear Systems

Recently a special hybrid system called Switching Markov Jump Linear System (SMJLS) is studied. A SMJLS is subject to a deterministic switching and a stochastic Markovain switching. To extend the results already obtained and to investigate some new aspects of such systems, our main contributions in this paper are: i) Transient analysis of Markov process, i.e., the expectations of the sojourn time, the activation number of any mode, and the number of switchings between any two modes and ii) two sufficient conditions of the exponential almost sure stability for a general SMJLS. Different from previous work, which is a special case of our study, the transition rate matrix for the random Markov process in our study is not fixed, but varies when a deterministic switching takes place.