Delay-dependent guaranteed cost control for uncertain discrete-time systems with delay

A guaranteed cost control problem for a class of discrete-time linear state-delayed systems with norm-bounded uncertainties is considered. Attention is focused on the design of memoryless state feedback controllers such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. By using a descriptor model transformation of the system and Moon´s inequality for bounding cross terms, new delay-dependent sufficient conditions for the existence of the guaranteed cost controller are presented in terms of linear matrix inequalities. Three numerical examples are given which show that the proposed method can even produce a lower guaranteed cost than the delay-independent methods.