Adaptive fuzzy H∞ stabilization for a class of nonlinear time-delay systems

In this paper, both indirect and direct adaptive fuzzy controllers with variable structure system (VSS) and H_infin performance are proposed for a class of nonlinear time-delay systems with unknown dynamics nonlinearities and external disturbances. It is assumed that the unknown nonlinear function of state-delays is bounded by a high-order function with unknown gains. An adaptive fuzzy controller design method is developed by using fuzzy logic systems to approximate unknown nonlinearities of the system dynamics, by using appropriate Lyapunov-Krasovskii functions to compensate for unknown time-delays and by combining VSS and H_infin control techniques. Furthermore, it is proved that the proposed design method can guarantee that all signals of the closed-loop system are uniformly ultimately bounded (UUB) and the robust H_infin performance is achieved. Finally, simulation examples are given to illuminate the effectiveness of the proposed approaches.