Static Gain Function-Based Adaptive Control for Nonlinear Systems with Unknown Time Delays

In this paper, the problem of global stabilization for a class of nonlinear strict-feedback time-delay systems is addressed by adopting the adaptive parameter estimation method and backstepping technique. The Lyapunov-Krasovskii functionals with static gain functions are designed in each step of the backstepping process. With the help of the sufficiently smooth projection operator, the relationship between the Lyapunov-Krasovskii functional and the previous virtual control laws is established. The memoryless adaptive control scheme guarantees that all the signals of the controlled system are globally uniformly ultimately bounded (GUUB). An illustrative example is provided to demonstrate the validity of the theoretical result.