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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 924107, 11 pages
http://dx.doi.org/10.1155/2012/924107
Research Article

The Stability of Nonlinear Differential Systems with Random Parameters

1Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech Republic
2Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, 60200 Brno, Czech Republic
3Department of Mathematics, Kyiv National Economic University, Peremogy Avenue 54/1, Kyiv 03038, Ukraine
4Department of Mathematics, University of Žilina, 01026 Žilina, Slovakia

Received 12 April 2012; Accepted 19 June 2012

Academic Editor: Agacik Zafer

Copyright © 2012 Josef Diblík 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.

Abstract

The paper deals with nonlinear differential systems with random parameters in a general form. A new method for construction of the Lyapunov functions is proposed and is used to obtain sufficient conditions for 𝐿 2 -stability of the trivial solution of the considered systems.