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

Bernard Brogliato 1 Andrey Polyakov 2, 3
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
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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Communication dans un congrès
54th Conference on Decision and Control 2015, Dec 2015, Osaka, Japan. IEEE, pp.5426-5431, 2016, 〈10.1109/CDC.2015.7403069〉
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Bernard Brogliato, Andrey Polyakov. Globally Stable Implicit Euler Time-Discretization of a Nonlinear Single-Input Sliding-Mode Control System. 54th Conference on Decision and Control 2015, Dec 2015, Osaka, Japan. IEEE, pp.5426-5431, 2016, 〈10.1109/CDC.2015.7403069〉. 〈hal-01212601〉

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