Global robust finite time stabilization of a class of nonlinear uncertain systems
一类不确定非线性系统的全局鲁棒有限时间镇定

A continuous global robust finite time feedback stabilization control law is proposed for a class of uncertain nonlinear systems. Firstly, a state feedback control law is designed for the nominal system. By using Lyapunov direct method and LaSalle invariance principle, we prove that the resulting closed-loop nominal system is globally asymptotically stable with the negative homogeneity in degrees. Secondly, introducing an auxiliary variable, we design a compensated control law for compensating the uncertainties of the system by using the finite-time convergent second-order sliding mode Super-twisting algorithm. The range of the parameters in the compensation control law is determined by using the finitetime Lyapunov function. Finally, a continuous feedback control law is developed for the closed-loop system to converge to its equilibrium point in a finite period of time. Simulation results show the effectiveness of the proposed control law.