New results for feedback control of discrete systems with time scales

The feedback control design problem for a wide class of discrete-time systems possessing fast and slow modes is considered in this paper. 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. Typical applications models are utilized to illustrate the design procedure and the simulation results validated the theoretical analysis.