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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 472430, 8 pages
http://dx.doi.org/10.1155/2013/472430
Research Article

Switched Convergence of Second-Order Switched Homogeneous Systems

Department of Mathematics, University of Cádiz, Campus of Puerto Real, 11510 Puerto Real, Spain

Received 14 June 2013; Accepted 16 August 2013

Academic Editor: Hamid Reza Karimi

Copyright © 2013 Carmen Pérez and Francisco Benítez. 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

This paper studies the stabilization of second-order switched homogeneous systems. We present results that solve the problem of stabilizing a switched homogeneous system; that is, we establish necessary and sufficient conditions under which the stabilization is assured. Moreover, given an initial condition, our method determines if there exists a switching law under which the solution converges to the origin and, if there exists this switching law, how it is constructed. Finally, two numerical examples are presented in order to illustrate the results.