Exponential stability of simultaneously triangularizable switched systems with explicit calculation of a common Lyapunov function

Asier Ibeas, Manuel de la Sen

Research output: Contribution to journalArticleResearchpeer-review

32 Citations (Scopus)

Abstract

In this note, a common quadratic Lyapunov function is explicitly calculated for a linear hybrid system described by a family of simultaneously triangularizable matrices. The explicit construction of such a function allows not only obtaining an estimate of the convergence rate of the exponential stability of the switched system under arbitrary switching but also calculating an upper bound for the output during its transient response. Furthermore, the presented result is then extended to the case where the system is affected by parametric uncertainty, providing the corresponding results in terms of the nominal matrices and uncertainty bounds. © 2009 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)1549-1555
JournalApplied Mathematics Letters
Volume22
DOIs
Publication statusPublished - 1 Oct 2009

Keywords

  • Common Lyapunov functions
  • Exponential stability
  • Robust stability
  • Switched systems

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