Robust guaranteed cost control for Markovian jump systems with time delay

This paper studies the problem of robust guaranteed cost control for the Markovian jump systems with time delay. The problem is to design a state feedback controller such that the closed-loop system is robustly stochastically stable and the closed-loop stochastic guaranteed cost function is not more than a specified upper bound for all admissible uncertainty and time delay. A criterion for the existence of such controller is derived based on the Lyapunov function combined with linear matrix inequalities (LMI). A parameterized characterization of the robust guaranteed cost controller is given in terms of the feasible solutions to the certain linear matrix inequalities. An example is presented to show that the result is efficient.