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

This paper addresses the problems of robust stability and stabilization of discrete-time linear systems with Markov jump parameters taking values in a countably infinite set. We consider the problem of robustness against complex multiperturbations, which extends the setting currently encountered in the literature. By means of the introduction of block-diagonal scaling techniques, we show how less conservative robust stability margins and robust controllers can be obtained by the solution of linear matrix inequality problems. The effectiveness of the main results is illustrated with a numerical example.