Growth rate of switched homogeneous systems

Tuna S. E.

AUTOMATICA, vol.44, no.11, pp.2857-2862, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 11
  • Publication Date: 2008
  • Doi Number: 10.1016/j.automatica.2008.03.017
  • Journal Name: AUTOMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2857-2862
  • Keywords: Homogeneity, Switched system, Growth rate, Joint spectral radius, Approximation algorithm, LYAPUNOV INDICATOR, STABILITY
  • Middle East Technical University Affiliated: Yes

Abstract

We consider discrete-time homogeneous systems under arbitrary switching and study their growth rate, the analogue of joint spectral radius for switched linear systems. We show that a system is asymptotically stable if and only if its growth rate is less than unity. We also provide an approximation algorithm to compute growth rate with arbitrary accuracy. (C) 2008 Elsevier Ltd. All rights reserved.