Lyapunov function design for finite-time convergence analysis: “Twisting” controller for second-order sliding mode realization

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.