Robust stabilization of discrete-time jump linear systems with multiplicative noise

This paper deals with the robustness of a class of discrete-time jump linear systems whose parameters are governed by a finite-state Markov chain and subject to piecewise deterministic and stochastic structured uncertainties. We establish that the exponential stability of this class is equivalent to the exponential stability of an associated class of discrete-time linear systems with no jumping parameters and subject to block diagonal deterministic and stochastic structured uncertainties. This key result is used to propose lower bounds for what we define as the stability radii with respect to this class of perturbation structures. The optimization problem of the stability radii that can be achieved by dynamic output feedback is also discussed and sufficient conditions are derived for the existence of stabilizing compensator which ensures that the stability radius is above a given level, via the resolution of parameterized matrix inequalities.