Robust Control for Two-Time-Scale Discrete Interval Systems

The problem of designing robust controller for discrete two-time-scale interval systems, conveniently represented using interval matrix notion, is considered. The original full order twotime-scale interval system is decomposed into slow and fast subsystems using interval arithmetic. The controllers designed independently to stabilize these two subsystems are combined to get a composite controller which also stabilizes the original full order two-time-scale interval system. It is shown that a state and output feedback control law designed to stabilize the slow interval subsystem stabilizes the original full order system provided the fast interval subsystem is asymptotically stable. The proposed design procedure is illustrated using numerical examples for establishing the efficacy of the proposed method.