A dwell time approach to the stability of switched linear systems based on the distance between eigenvector sets

Abstract

In this article, a sufficient condition on the minimum dwell time that guarantees the stability of switched linear systems is given. The proposed method interprets the stability of switched linear systems through the distance between the eigenvector sets of subsystem matrices. Thus, an explicit relation in view of stability is obtained between the family of the involved subsytems and the set of admissible switching signals.

Keywords:

• switched systems
• dwell time
• stability
• eigenvector sets

Acknowledgement

This work is partly supported by the Scientific and Technological Research Council of Turkey (TUBITAK BAYG). We would like to thank Külmiz Çevik for the valuable discussions we carried out with him on the stability of switched systems and Ulrich Steinmetz for the information he shared with us on the properties of normal matrices. We would also like to thank the anonymous reviewers, whose comments improved the quality of the article.