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Globally Stable Implicit Euler Time-Discretization of a Nonlinear Single-Input Sliding-Mode Control System

Authors
  • Brogliato, Bernard
  • Polyakov, Andrey
Publication Date
Dec 15, 2015
Source
HAL-UPMC
Keywords
Language
English
License
Unknown
External links

Abstract

In this note we study the effect of an implicit Euler time-discretization method on the stability of the discretization of a globally fixed-time stable, scalar differential inclusion representing a simple nonlinear system with a set-valued signum controller. The controller nonlinearity is a cubic term and it is shown that the fully-implicit method preserves the global Lyapunov stability property of the continuous-time system, contrarily the explicit discretization which does not. It allows to obtain finite-time convergence to the origin when the plant is undisturbed, while the cubic term provides the hyper-exponential convergence rate.

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