Second order twisting algorithms via singularization of local first order sliding regimes

Abstract

Using Lyapunov functions, Vadim Utkin proposed and demonstrated that some higher-order sliding regime characteristics can be obtained via first-order sliding modes. In this work, using an elementary differential geometric setting, we demonstrate that prototypical second-order sliding algorithms (namely: the twisting and the super-twisting algorithms) can be obtained via a limiting procedure, exercised on a suitably parameterized linear sliding surface in the plane, that singularizes to the origin of coordinates the region of local existence of a first-order sliding regime induced on certain second order switch controlled dynamics.