Mathematical Problems in Engineering
Volume 7 (2001), Issue 1, Pages 15-27

A generalized regular form for multivariable sliding mode control

W. Perruquetti, J. P. Richard, and P. Borne

Laboratory of Automatic Control (LAIL UPRESA CNRS 8021), Ecole Centrale de LILLE, BP 48, 59 651 Villeneuve d'Ascq Cedex, France

Received 18 July 2000

Copyright © 2001 W. Perruquetti et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper shows how to compute a diffeomorphic state space transformation in order to put the initial mutivariable nonlinear model into an appropriate regular form. This form is an extension of the one proposed by Lukyanov and Utkin [9], and constitutes a guidance for a “natural” choice of the sliding surface. Then stabilization is achieved via a sliding mode strategy. In order to overcome the chattering phenomenon, a new nonlinear gain is introduced.