Robust stabilization of jump linear systems with multiplicative noise

This paper deals with the robustness of stability and stabilization problem for a class of jump linear systems with Markov jumping parameters and subject to piecewise deterministic and stochastic uncertainties. We prove that the exponential stability of these systems is equivalent to exponential stability of associated linear Itô systems with no jumping parameters subject to structured block‐diagonal multi‐perturbations. This result is exploited to give lower bounds for what we define as the stability radii of this type of systems, via the resolution of parametrized linear matrix inequalities. The optimization problem by output feedback is also addressed. Sufficient conditions are presented for the existence of a stabilizing dynamic full‐order controller, which ensure that the closed‐loop system has a stability radius greater than some pre‐specified bound, and a procedure for the construction of stabilizing compensator is proposed via the resolution of a number of linear matrix inequalities. The paper ends with a brief discussion of the state feedback case.