When is a set of LMIs a sufficient condition for stability

Amir Ali Ahmadi, Raphaël M. Jungers, Pablo A. Parrilo, Mardavij Roozbehani

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations


We study stability criteria for discrete time switching systems and provide a meta-theorem that characterizes all the LMI-based Lyapunov theorems. For this purpose, we investigate the structure of sets of LMIs that are a sufficient condition for stability (i.e., such that any switching system which satisfies these LMIs is stable). Different such LMI conditions have been proposed in the last fifteen years, and we prove in this paper that a family of conditions recently provided by us actually encapsulates all the possible valid conditions. As a byproduct, we show that it is PSPACE-complete to recognize whether a particular set of LMIs implies the stability of a switching system.

Original languageEnglish (US)
Title of host publicationROCOND'12 - 7th IFAC Symposium on Robust Control Design
PublisherIFAC Secretariat
Number of pages6
EditionPART 1
ISBN (Print)9783902823038
StatePublished - 2012
Externally publishedYes
Event7th IFAC Symposium on Robust Control Design, ROCOND'12 - Aalborg, Denmark
Duration: Jun 20 2012Jun 22 2012

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
ISSN (Print)1474-6670


Other7th IFAC Symposium on Robust Control Design, ROCOND'12

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering


  • Convex optimization
  • Finite automata
  • Hybrid systems
  • Joint spectral radius
  • Linear matrix inequalities


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