A geometric approach to composite control of two-time-scale systems

The basic results from center manifold theory ([1], [2], [3], [4]) are applied to singularly perturbed nonlinear control systems. Under certain assumptions, the existence of a local, control dependent, invariant manifold allows us to relate asymptotic properties as t ⟶ ∞ of the singularly perturbed control system to those of a reduced order control system. Moreover, with the use of composite control strategy, the asymptotic properties as ε ⟶ 0 of the original control system and the reduced order one are also related via a version of Tikhonov's theorem given in [13].