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Mathematical Problems in Engineering
Volume 2006, Article ID 17837, 15 pages

Stability of differential inclusions: A computational approach

Institute for Automation Technology (IFAT) Department of Electrical Engineering, Otto-von-Guericke University of Magdeburg, P.O. Box 4120, Magdeburg 39016, Germany

Received 8 October 2004; Revised 27 December 2004; Accepted 20 April 2005

Copyright © 2006 Vadim Azhmyakov. 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.


We present a technique for analysis of asymptotic stability for a class of differential inclusions. This technique is based on the Lyapunov-type theorems. The construction of the Lyapunov functions for differential inclusions is reduced to an auxiliary problem of mathematical programming, namely, to the problem of searching saddle points of a suitable function. The computational approach to the auxiliary problem contains a gradient-type algorithm for saddle-point problems. We also extend our main results to systems described by difference inclusions. The obtained numerical schemes are applied to some illustrative examples.