Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays

The guaranteed cost control problem is studied in this paper for a class of uncertain linear discrete-time systems with both state and input delays and a given quadratic cost function. The uncertainty in the system is assumed to be norm-bounded and time-varying. 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 controllers are derived based on the linear matrix inequality (LMI) approach, a parametrized characterization of the guaranteed cost controllers (if they exist) is given in terms of the feasible solutions to a certain LMI. Furthermore, a convex optimization problem is formulated to select the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.