ON A STATE-SPACE APPROACH IN ROBUST-CONTROL FOR SINGULARLY PERTURBED SYSTEMS

A direct state-space approach for an estimate of the graph metric of s ingularly perturbed systems (SPS) is proposed. Based on a new version of the Tikhonov Theorem on uniform convergence of the slow variables i n a stable SPS over the unit ball of inputs in L(2), an estimate of th e first order to the small parameter for a graph metric between SPS an d its 'state decoupled form' is obtained for both time varying and tim e invariant cases. Moreover, a similar estimate of a graph metric betw een SPS and its slow system when the fast system satisfies some additi onal conditions is given. Furthermore, the robust state feedback H-inf inity control for SPS is also considered in an analogous manner. An ad vantage there is that infinitely many composite feedback controls are obtained directly, bypassing the traditional arguments used in SPS the ory such as approximation of solutions of Riccati equations and the Im plicit function theorem.