On the robust stability, stabilization, and stability radii of continuous-time Markov jump linear systems

This paper addresses the robust stability and stabilization of continuous-time linear systems with Markov jump parameters taking values in a finite set. It is shown how each of the robust analysis and synthesis problems can be expressed in terms of two alternative linear matrix inequalities, in which the scaling parameters appear as decision variables. As a by-product, new contributions to the theory of stability radii of Markov jump linear systems are provided. Some numerical examples illustrate the main results presented here.