Stability Analysis of Polytopic Markov Jump Linear Systems with Applications to Sequence-Based Control over Networks

Abstract

This paper deals with sequence-based control over networks with time-varying and generally unknown delay and loss probabilities. We show that the problems of stability analysis and controller synthesis can be addressed using a polytopic Markov jump linear system describing an augmented system. For this kind of systems, we derive a necessary and sufficient condition for mean square stability that extends existing results in literature. Likewise, we provide a sufficient condition for mean square stabilizability in terms of an LMI feasibility test. The results are illustrated in a numerical example.