Robust stability and stabilization of continuous-time infinite Markov jump linear systems

This paper addresses the robust stability and stabilization problems for a class of continuous-time linear systems with Markov jump parameters taking values in a countably infinite set. We consider the problem of robustness against various classes of parametric uncertainty, which extends previous results in the literature. By means of the introduction of novel scaling techniques, it is shown how less conservative robust stability margins and robust controllers can be obtained by the solution of linear matrix inequality problems. The effectiveness of the obtained results is illustrated with a numerical example.