Feedback control of a class of nonlinear singularly perturbed systems with time delay

The feedback control of two classes of nonlinear time-delay singularly perturbed systems with fast actuators is considered. First, by means of the integral manifold method, the asymptotic stability of a class of nonlinear time-delay singularly perturbed systems can be guaranteed and the phase trajectories of the closed-loop systems are steered along the integral manifold to the origin. Second, a continuous state feedback controller is constructed such that the trajectories of a class of uncertain nonlinear time-delay singularly perturbed feedback-controlled systems are uniformly ultimately bounded. We require no a priori information on the uncertain element, except that its restraint set is assumed to be known and compact.

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