H∞-guaranteed cost control for linear systems with time-delay

Solving state feedback H_infin control problem usually leads to controller gain too large. A effective method to solve the problem is simultaneously to introduce guaranteed cost control. The delay-dependent H_infin -guaranteed cost control problem for linear systems with state delay is investigated. A delay-dependent condition for the existence of H_infin and guaranteed cost memoryless state feedback controller is presented in terms of matrix inequality such that the resulting closed-loop system is asymptotically stable and guarantees H_infin performance index, and an upper bound on the given cost function can be obtained. Furthermore, a design method of the optimal H_infin-guaranteed cost controller is given against the constant initial value. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed results.