Optimal guaranteed cost control for nonlinear discrete-time uncertain systems with state delay

This paper studies the guaranteed cost control problem for a class of nonlinear discrete-time uncertain systems with state delay and a given quadratic cost function. The problem is to design a memoryless state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controller are derived based on the linear matrix inequality (LMI) approach, a parameterized characterization of the guaranteed cost controller is given in terms of the feasible solutions to a certain LMI.