Unified optimization of H-infinity — Guaranteed cost control for linear systems with time-delay

The delay-dependent H-infinity guaranteed cost control problem for linear systems with state delay is considered. A delay-dependent condition for the existence of H-infinity guaranteed cost state feedback controller is presented in terms of linear matrix inequality such that the resulting closed-loop system is asymptotically stable and guarantees H-infinity performance index. It can be proved that the condition also satisfies the requirement of guaranteed cost control and an upper bound on the given cost function can be obtained. Furthermore, a design method of the optimal H-infinity-guaranteed cost control law is given against the constant initial value. Finally, numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed results.