Robust Stabilization of Single Nonlinear Time-Delay System

Abstract

The problem of robust stabilization for a class of uncertain dynamic systems with multiple delayed state perturbations is considered. It is assumed that perturbations of the time-delay sections are not bounded by first-order linear functions, but bounded by high-order functions with unknown gains. And the time delay considered is time varying. Two classes of controllers are proposed. When the time derivative of each time-varying time delay is less than one, a class of adaptive state feedback controllers are proposed based on Lyapunov–Krasovskii method, which can render the closed-loop systems uniformly ultimately bounded stable. Novel nonlinear feedback controllers are developed by employing Razumikhin lemma, and the controller also can render the closed-loop systems stable in the sense of uniform ultimate boundedness. Finally, several examples are given to show the potential of the proposed techniques.