Mean square stability of Markov Jump Linear Systems with piecewise constant transition rates under dwell-time specifications

This paper deals with the stability of a class of Markov Jump Linear Systems characterized by piecewise-constant transition rates and system dynamics. These systems are called Switching Markov Jump Linear Systems. Mean square stability analysis is carried out by studying the time evolution of the second-order moment of the state. A sufficient condition guaranteeing mean square stability under constraints on the dwell-time between switching instants is derived. It is shown that such a condition, as well as another one based on Kronecker calculus, admit an LMI implementation.