The Method of Characteristics for the Lyapunov Function Design in the Finite-Time Stability Analysis of Sliding Mode Controlled Systems with Uncertainties

摘要

This presentations deals with designing of Lyapunov functions for the analysis of a finite-time stabilization of the class of nonlinear systems containing the, so-called, second order type sliding-mode controllers. The design of the corresponding Lyapunov functions is based on the solution of a specic Partial Differential Equation (PDE) which can be resolved by the application of "Method of Characteristics" transforming the considered PDE into a system of Ordinary Didderential Equations (ODE). The collection of the first integrals of this ODE-system permits to find an analytical expression for the desired Lyapunov Function, in particular, for "twisting", "super-twisting" and "nested" (imbedded) controllers. This paper presents the survey of the works fulfilled in CINVESTAV-IPN during three last years.