Mathematical Problems in Engineering
Volume 3 (1996), Issue 1, Pages 1-25

Lyapunov analysis of sliding motions: Application to bounded control

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

Ecole Centrale de LILLE, LAIL-URA CNRS D 1440, BP 48, Villeneuve d'Ascq CEDEX 59651, France

Received 15 January 1995

Copyright © 1996 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 results concern the fundamental problem of Lyapunov analysis of sliding motions. It consist first to estimate the useful part of the sliding surface (the so-called “sliding domain”) and second to estimate the useful part of the state domain that is the domain of all initial conditions for which the corresponding solutions converge to the sliding domain. The application of such results concern the design of a realistic bounded control. Several examples are exposed in order to illustrate the obtained results.