H2 and H∞ control of discrete systems with time scales

This paper addresses the feedback control design problem for a wide class of discrete-time systems possessing fast and slow modes. The slow and fast subsystems are considered to be completely controllable and observable. Based on the H_∞ optimization criteria, a two-stage design procedure is developed using separate gain matrices for the fast and slow subsystems and computed using linear matrix inequalities. A composite control is designed to yield first-order approximations to the behavior of the discrete system. A typical application is presented to illustrate the design procedure.