Abstract: The problem of adaptive stabilization for a class of nonlinear systems including matching time varying delayed disturbance is discussed. The bound of the time varying delayed state disturbances are unknown, and are assumed to satisfy the linear growth conditions. By using the Lyapunov stability theory and Lyapunov Krosovskii functional, we propose a robust adaptive state feedback controller, which can guarantee that the closed loop system is globally stable in the sense of uniform ultimate boundedness, and the state trajectories uniformly asymptotically tend to zero. An illustrative example is given to demonstrate validity of the results.

Key words: time varying delayed disturbance, nonlinear systems, adaptive control, Lyapunov Krosovskii functional, uniform ultimate boundedness