Stability of Markov regenerative switched linear systems

In this paper we give a necessary and sufficient condition for the 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, includes various switched linear systems including Markov jump linear systems and semi-Markov jump linear systems. We show that a Markov regenerative switched linear system is mth mean stable if and only if a matrix is Schur stable, under the assumption that either m is even or the system is positive.