Guaranteed Cost Control for a Class of Nonlinear Discrete Time-Delay Systems

The guaranteed cost control problem for a class of nonlinear discrete time-delay systems is investigated. Based on the Lyapunov matrix, a complete-type Lyapunov-Krasovskii functional is constructed. Thereby, the Lyapunov stability theory is employed to design the exact form of the controller to ensure that the resultant closed-loop system is asymptotically stable and the cost function is bounded. A numerical example is presented to illustrate the usefulness of the theoretical results.