Analysis and synthesis of uncertain switched discrete-time systems

Magdi S. Mahmoud, Mohamed Nounou, Hazem Nounou

Research output: Contribution to journalArticle

24 Citations (Scopus)


The problems of L2-gain analysis and control synthesis for a class of linear discrete-time switched systems with convex-bounded parameter uncertainties in all system matrices are investigated. The main thrust is based on the constructive use of an appropriate switched Lyapunov functional. The L2-gain analysis is to characterize conditions under which the linear switched system with polytopic uncertainties is uniformly quadratically stable with an L2 gain smaller than a prescribed constant level. The control synthesis is to design switched feedback schemes, whether based on state-, output measurements or by using dynamic output feedback, to guarantee that the corresponding closed-loop system enjoys the uniform quadratic stability with an L2 gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over linear matrix inequalities and tested on representative examples.

Original languageEnglish
Pages (from-to)245-257
Number of pages13
JournalIMA Journal of Mathematical Control and Information
Issue number2
Publication statusPublished - Jun 2007



  • Lmis
  • Polytopic uncertainty
  • Switched output feedback
  • Switched state feedback
  • Switched systems
  • Uniform quadratic stability

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Systems Engineering
  • Control and Optimization

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