Mathematical Problems in Engineering
Volume 4 (1999), Issue 6, Pages 461-487

The simplex method for nonlinear sliding mode control

G. Bartolini,1 F. Parodi,2 V. I. Utkin,3 and T. Zolezzi4

1Istituto di Elettrotecnica, Universita' di Cagliari, Piazza d'Armi, Cagliari 09123, Italy
2IMI, Universita' di Genova, P. Kennedy Pad.D, Genova 16129, Italy
3Department of Electrical Engineering, The Ohio State University, Columbus 43210-1275, Ohio, USA
4DIMA, Universita' di Genova, via Dodecaneso 35, Genova 16146, Italy

Received 30 October 1997; Revised 17 June 1998

Copyright © 1999 G. Bartolini 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.


General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.