On the design of stabilizing controller for uncertain two-time-scale discrete systems

We consider design of stabilizing controller for linear structured uncertain discrete two-time-scale system which can be represented by the interval matrix representation. The slow and fast uncertain subsystems are obtained using interval arithmetic. It is shown that a state feedback and output feedback control law designed to stabilize the slow uncertain subsystem will stabilize the original full order system, provided that fast uncertain subsystem is asymptotically stable. The results obtained are illustrated by a numerical example