Mathematical Problems in Engineering

Mathematical Problems in Engineering / 1999 / Article

Open Access

Volume 4 |Article ID 851687 |

G. Bartolini, F. Parodi, V. I. Utkin, T. Zolezzi, "The simplex method for nonlinear sliding mode control", Mathematical Problems in Engineering, vol. 4, Article ID 851687, 27 pages, 1999.

The simplex method for nonlinear sliding mode control

Received30 Oct 1997
Revised17 Jun 1998


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.

Copyright © 1999 Hindawi Publishing Corporation. 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.

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