Stability of Markov regenerative switched linear systems

In this paper, we give a necessary and sufficient condition for mean stability of switched linear systems having a Markov regenerative process as its switching signal. This class of switched linear systems, which we call Markov regenerative switched linear systems, contains Markov jump linear systems and semi-Markov jump linear systems as special cases. We show that a Markov regenerative switched linear system is $m$th mean stable if and only if a particular matrix is Schur stable, under the assumption that either $m$ is even or the system is positive.