Input–Output Stochastic Stability for Markov Jump Linear Systems

Among several stability notions for dynamical systems, input–output stability is significant in applications where one is interested in the input–output relation rather than in the internal dynamics. This article addresses a notion of input-output stability for Markov jump linear systems and presents a testable, necessary and sufficient condition. Examples show that this stability notion is weaker than stochastic stability (a usual notion of stability for the considered class of systems), and an illustrative control problem finds input–output stabilizing gains in a system that is not stochastically stabilizable.