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Mathematical Problems in Engineering
Volume 2013, Article ID 948147, 9 pages
http://dx.doi.org/10.1155/2013/948147
Research Article

Upper Bounds for the Distance between a Controllable Switched Linear System and the Set of Uncontrollable Ones

Escola Tècnica Superior d'Enginyeria Industrial Barcelona, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain

Received 27 February 2013; Revised 2 May 2013; Accepted 7 May 2013

Academic Editor: Xiaojie Su

Copyright © 2013 Josep Clotet and M. Dolors Magret. 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 set of controllable switched linear systems is an open and dense set in the space of all switched linear systems. Therefore it makes sense to compute the distance from a controllable system to the nearest uncontrollable one. In the case of a standard system, , R. Eising, D. Boley, and W. S. Lu obtain some results for this distance, both in the complex and real cases. In this work we explore this distance, for switched linear systems in the real case, obtaining upper bounds for it. The main contribution of the paper is to prove that a natural generalization of the upper bound obtained by D. Boley and W. S. Lu is true in the case of switched linear systems.