Mathematical Problems in Engineering 
Volume 4 (1999), Issue 6, Pages 461-487
doi:10.1155/S1024123X98000921

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

Abstract

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.