Stabilizing feedbacks for imperfectly known, singularly perturbed nonlinear systems with discrete and distributed delays

Abstract

A class of nonlinear memoryless controllers is synthesized to guarantee global uniform ultimate boundedness, with respect to some known set, for a class of imperfectly known singularly perturbed nonlinear systems, with discrete and distributed delays, provided that the singular perturbation parameter is small enough. Each feedback controller is designed using information based mainly on a nonlinear, affine in the control, ‘reduced-order’ system. The uncertainty, which may be time, state, delayed state and/or input dependent, is modelled by additive nonlinear perturbations influencing a known nominal, singularly perturbed time-delay system of the retarded type. A ‘matched’ uncertainty structural condition for the reduced-order system is not presumed in this paper.