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Finite-time Stabilization Using Implicit Lyapunov Function Technique

Andrey Polyakov 1 Denis Efimov 1, 2 Wilfrid Perruquetti 1, 2
1 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
2 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : The Implicit Lyapunov Function (ILF) method for finite-time stability analysis is introduced. The control algorithm for finite-time stabilization of a chain of integrators is developed. The scheme of control parameters selection is presented by a Linear Matrix Inequality (LMI). The robustness of the finite-time control algorithm with respect to system uncertainties and disturbances is studied. The new high order sliding mode (HOSM) control is derived as a particular case of the developed finite-time control algorithm. The settling time estimate is obtained using ILF method. The algorithm of practical implementation of the ILF control scheme is discussed. The theoretical results are supported by numerical simulations.
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https://hal.inria.fr/hal-00844386
Contributor : Denis Efimov <>
Submitted on : Monday, July 15, 2013 - 10:40:21 AM
Last modification on : Tuesday, September 29, 2020 - 12:24:14 PM
Long-term archiving on: : Wednesday, October 16, 2013 - 4:14:23 AM

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Andrey Polyakov, Denis Efimov, Wilfrid Perruquetti. Finite-time Stabilization Using Implicit Lyapunov Function Technique. IFAC Nolcos 2013, Sep 2013, Toulouse, France. ⟨hal-00844386⟩

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