Stability of switched linear discrete-time descriptor systems: A new commutation condition

Guisheng Zhai, Xuping Xu, Daniel W.C. Ho

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


In this article, we study stability of switched linear discrete-time descriptor systems. Under the assumption that all subsystems are stable and there is no impulse occurring at the switching instants, we establish a new pairwise commutation condition under which the switched system is stable. It turns out that the condition is a natural and important extension to the existing commutation conditions, and it can be applied in discretised continuous-time switched systems in a straightforward manner. Finally, we also show that when the proposed commutation condition holds, there exists a common quadratic Lyapunov function for the subsystems.

Original languageEnglish
Pages (from-to)1779-1788
Number of pages10
JournalInternational Journal of Control
Issue number11
Publication statusPublished - 2012 Nov 1


  • common quadratic Lyapunov functions
  • impulse-free switching
  • matrix inequalities
  • pairwise commutation
  • stability
  • switched linear discrete-time descriptor systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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