Lyapunov function design for finite-time convergence analysis: "Twisting" controller for second-order sliding mode realization
Lyapunov function design for finite-time convergence analysis: "Twisting" controller for second-order sliding mode realization
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DOI：
10.1016/j.automatica.2008.07.013
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发表时间：
2009-02
期刊：
影响因子：
--
通讯作者：
A. Polyakov;A. Poznyak
中科院分区：
文献类型：
--
作者：
A. Polyakov;A. Poznyak
给出了Lyapunov函数设计的Zubov方法的推广。它是基于特征线法的应用，涉及一类特殊类型的一阶偏微分方程解。这个方程的成功解保证了右端不连续的常微分方程所给出的相应动力学方程的有限时间收敛。文中给出了该方法在“扭转”控制器稳定性分析中的应用。给出了所构造的Lyapunov函数及其水平线截面图。
A generalization of the Zubov method of a Lyapunov function design is presented. It is based on the characteristic method application and is related to resolving the first-order partial differential equation of a special type. A successful resolution of this equation guaranties a finite-time convergence for the corresponding dynamics given by an ordinary differential equation with a discontinuous right-hand side. The suggested method is illustrated by its application to the so-called “twisting” controller stability analysis. The constructed Lyapunov function as well as its level line sections is graphically illustrated.