A bounded real lemma for jump systems

This note presents a bounded real lemma for discrete-time Markovian jump linear systems (MJLSs). We show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems. For the case of one plant mode, this condition reduces to the standard necessary and sufficient condition for discrete-time systems. We envision this lemma being used to construct necessary and sufficient analysis and synthesis conditions for MJLSs.