Delay dependent guaranteed cost control for linear systems with time-delay

The delay dependent guaranteed cost control problem via memoryless state feedback controllers is studied for a class of linear systems with time-delay and a given quadratic cost functional. By using the Lyapunov stability theory, optimal control theory, and linear matrix inequality (LMI), a simple design approach on delay dependent guaranteed cost controller is proposed. The guaranteed cost controller can be obtained through the solution of a Riccati matrix equation. An upper bound on the cost function is provided, which is dependent on the time-delay size of the system. As the time-delay size is equal to zero, the upper bound of the cost function is equal to the optimal cost function value.