Analysis of finite-time convergence by the method of Lyapunov functions in systems with second-order sliding modes

A method for constructing Lyapunov functions for analysing of control systems with second-order sliding modes is proposed. It is based on solving a special partial differential equation and enables Lyapunov functions to be constructed that prove that a system transfers into a sliding mode after a finite time and give an explicit estimate of this time. The method is illustrated for three known second order sliding algorithms.