Almost sure stability of discrete‐time Markov jump linear systems

Abstract

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.