Adaptive robust control based on Lyapunov-Razumikhin function for uncertain nonlinear time-delay systems

Abstract

This paper investigates adaptive stabilization problem for nonlinear time-delay systems with parametric uncertainty. A LaSalle-Yoshizawa-like theorem established on LaSalle-Razumikhin invariant set theorem is given, which provides a sufficient condition for the convergence of the partial states with boundedness of the time-delay system. Using the proposed theorem, an adaptive stabilizing controller is derived for uncertain nonlinear time-delay systems. Moreover, it is also shown that the adaptive stabilization problem for the nonlinear time-delay system with strict parametric-feedback form can be solved by recursively constructing Lyapunov-Razumikhin function satisfying the proposed condition.