Almost sure stability of discrete-time Markov jump linear systems

This study deals with a transient analysis and almost sure stability for the discrete-time Markov jump linear systems (MJLS). The expectation of the sojourn time and the activation number of any mode and the switching number between any two modes of the discrete-time MJLS are presented firstly. Then, an analysis of the transient behaviour is given. Finally, a new deterministically testable condition for the exponentially almost sure stability is proposed.