Infinite Markov jump-bounded real lemma

A bounded real lemma is established, providing an equivalent condition to stochastic stability (SS) of a continuous-time infinite Markovian jump linear system (MJLS) with a prescribed L2L2-stochastic disturbance attenuation level γγ in terms of existence of solutions to an infinite set of coupled linear matrix inequalities (LMIs). Besides the interest in its own right, the main result provides a fundamental tool for the development of an H∞H∞-like theory devoted to this class of systems.