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 L₂-stochastic disturbance attenuation level γ 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_∞-like theory devoted to this class of systems.