Adaptive fuzzy tracking control for a class of nonlinear time-varying delay systems

In this paper, adaptive fuzzy tracking control is proposed for a class of uncertain SISO nonlinear time-varying delay systems in a Brunovsky form with unknown nonlinear dead-zone input. It is shown that the dead-zone output can be represented as a simple linear system with a static time-varying gain and bounded disturbance by introducing characteristic function. The unknown time-varying delay uncertainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. By utilizing the integral-type Lyapunov function and introducing a continuous function, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded.