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 singularly perturbed systems (SPS) is proposed. Based on a new version of the Tikhonov Theorem on uniform convergence of the slow variables in a stable SPS over the unit ball of inputs in L(2), an estimate of the first order to the small parameter for a graph metric between SPS and its 'state decoupled form' is obtained for both time varying and time invariant cases. Moreover, a similar estimate of a graph metric between SPS and its slow system when the fast system satisfies some additional conditions is given. Furthermore, the robust state feedback H-infinity control for SPS is also considered in an analogous manner. An advantage there is that infinitely many composite feedback controls are obtained directly, bypassing the traditional arguments used in SPS theory such as approximation of solutions of Riccati equations and the Implicit function theorem.