Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays

This note concerns the robust guaranteed cost control problem for a class of continuous-time Markovian jump linear system with norm-bounded uncertainties and mode-dependent time-delays. The problem is to design a memoryless state feedback control law such that the closed-loop system is stochastically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on linear matrix inequality, delay-dependent sufficient conditions for the existence of such controller are derived by using a descriptor model transformation of the system and by applying Moon´s inequality for bounding cross terms. Sufficient conditions which depend on the difference between the largest and the smallest time-delays are also presented. Two numerical examples are given for illustration of the proposed theoretical results.