Robust sliding mode control of nonlinear systems with delay: A design via polytopic formulation

Frédéric Gouaisbaut 1 Yann Blanco 2 Jean-Pierre Richard 3, 4
3 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
4 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : This paper outlines the possibility to control nonlinear uncertain systems with single, possibly time-varying state-delay. These systems are submitted to additive perturbations (possibly nonvanishing). The control is of sliding mode type and the sliding surface is designed so to maximize the calculable set of delays which do not destabilize the system. The way to deal with the nonlinear parts of the model relies on a polytopic formulation. The conditions for the existence of the sliding regime are studied by using both a Lyapunov-Krasovskii functionnal and a Lyapunov-Razumikhin function. The optmization precedure for the choice of the sliding surface is expressed in terms of LMIs. An example illustrates the proposed method.
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https://hal.inria.fr/inria-00266509
Contributor : Jean-Pierre Richard <>
Submitted on : Sunday, March 23, 2008 - 10:00:00 PM
Last modification on : Friday, June 14, 2019 - 6:31:01 PM
Long-term archiving on : Friday, May 21, 2010 - 12:49:48 AM

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  • HAL Id : inria-00266509, version 1

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Frédéric Gouaisbaut, Yann Blanco, Jean-Pierre Richard. Robust sliding mode control of nonlinear systems with delay: A design via polytopic formulation. International Journal of Control, Taylor & Francis, 2004, 77 (2), pp.206-215. ⟨inria-00266509⟩

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