Adaptive variable structure control of time-varying delay nonlinear systems

In this paper, adaptive variable structure control is proposed for a class of time-varying delay nonlinear systems with unknown constant control gain. The unknown function and the upper bound of the unknown time delay term are assumed to be in the form of nonlinear functions with unknown coefficients. The uncertain time delay terms are compensated for using appropriate Lyapunov-Krasovskii functional and Young´s inequality in the design. The closed loop control system is proved to be semi globally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the approach.