Sign-stability of Positive Markov Jump Linear Systems

This paper investigates stability of Positive Markov Jump Linear Systems (PMJLSs) in the absence of a numerical realization. It considers the situation when only signs (and not magnitudes) of the entries of the subsystem matrices and the Markov transition matrices are known. The result is an analysis of a qualitative notion of stability known as sign-stability. Although the notions of sign-stability of PMJLSs are natural extensions of standard stochastic stability concepts such as exponential almost sure, mean and mean-square stability, the sign-stability notions are proven equivalent, which is not the case for their corresponding standard concepts. Moreover, for irreducible Markov chains, the particular structure of the Markov chain is shown to have no bearing on sign-stability.