Optimal guaranteed cost control of uncertain discrete-time systems with delayed state

摘要

The guaranteed cost control problem via state feedback is studied in this paper for a class of uncertain discrete-time systems with delayed state and a given quadratic cost function. The uncertainty in the system is assumed to be norm-bounded and time-varying. It is proved that the feasibility of a linear matrix inequality (LMI) problem is necessary and sufficient for the existence of guaranteed cost controllers, and a parametrized characterization of the guaranteed cost controllers (if they exist) is given in terms of the feasible solutions to this 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.