Delay-dependent guaranteed cost control for uncertain discrete-time systems with both state and input delays

This paper considers the guaranteed cost control problem for a class of uncertain linear discrete-time systems with both state and input delays. By representing the time-delay system in the descriptor system form and using a recent result on bounding of cross products of vectors, we obtain new delay-dependent sufficient conditions for the existence of the guaranteed cost controller in terms of linear matrix inequalities. Numerical examples are presented which shows that the proposed method can even produce a lower guaranteed cost than the delay-independent methods.