Guaranteed cost control of uncertain discrete linear time-delay systems

Considers guaranteed cost control problem for a class of uncertain discrete-time linear systems with state delay. The uncertainty is assumed to be norm-bounded, and the attention is focused on the design of memoryless state feedback controllers such that the resulting closed-loop system is not only asymptotically stable but also guarantees an adequate level of performance. A sufficient condition for the existence of guaranteed cost controllers is derived and a parametrized characterization of guaranteed cost control laws is given in terms of the feasible solutions to a certain linear matrix inequality