Prescribed finite-time stabilization of fuzzy neural networks with time-varying controller

Abstract

This paper investigates the exponential and prescribed finite-time stabilization with time-varying controller. First, the constraints of boundedness and differentiability on time delays are simultaneously relaxed, the Lipschitz condition for activation function is also relaxed. Second, different from the traditional Lyapunov function, two different time-varying Lyapunov functions are respectively constructed to achieve the exponential and prescribed finite-time stabilization. Significantly, the exponential convergence rate and the settling time are constants that can be given in advance and are not affected by system parameters and initial states. In addition, the time-varying controllers have good tolerance for disturbance caused by discontinuous functions and the disturbance is perfectly resolved and does not affect the control performance. Especially, the form of controllers is relatively simple and there is not necessary to design the fractional-order controllers for prescribed finite-time stabilization. Furthermore, the exponential and prescribed finite-time stabilization for FNNs without delay are respectively established via continuous time-varying state feedback control. Finally, examples show the effectiveness of the proposed control methods.