Dynamic output compensator design for time-varying discrete time systems with delayed states

Convex conditions, proposed as a feasibility test of a set of linear matrix inequalities (LMIs), are given for the design of a partially parameter dependent dynamic output feedback controller for a class of discrete time systems with delayed state. This class concerns the systems with time-varying delay in the state and time varying parameters, both assumed to be available on line. The controller is composed by a classical part, feeding-back the system output and another one where the delayed output of the system is feedback. This last part can be avoided in case of inaccessible delay value, resulting in a more classical control design. Different from other approaches found in the literature, it is used a parameter dependent Lyapunov-Krasovskii functional candidate and a slack matrix variable to reduce the conservatism of the proposed approach. The resulting parameter dependent controller can be obtained on line as a convex combination of some “vertex” controllers. Numerical examples are presented to illustrated the effectiveness of the proposal.