Mathematical Problems in Engineering 
Volume 7 (2001), Issue 1, Pages 15-27
doi:10.1155/S1024123X01001508

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

Abstract

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.