A Bounded Real Lemma for Jump Systems

Pete Seiler, Raja Sengupta

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This note presents a bounded real lemma for discrete-time Markovian jump linear systems (MJLSs). We show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems. For the case of one plant mode, this condition reduces to the standard necessary and sufficient condition for discrete-time systems. We envision this lemma being used to construct necessary and sufficient analysis and synthesis conditions for MJLSs.

Original languageEnglish (US)
Pages (from-to)1651-1654
Number of pages4
JournalIEEE Transactions on Automatic Control
Issue number9
StatePublished - Sep 2003

Bibliographical note

Funding Information:
Manuscript received June 17, 2002; revised February 2, 2003. Recommended by Associate Editor C. D. Charalambous. This work was supported in part by the Office of Naval Research (ONR) under Grant N00014-00-1-0621. P. Seiler is with the Department of Mechanical and Industrial Engineering, University of Illinois, Urbana-Champaign, Urbana, IL 61801 USA (e-mail: pseiler@uiuc.edu). R. Sengupta is with the Department of Civil Engineering, University of California, Berkeley, Berkeley, CA 94720 USA (e-mail: raja@path.berkeley.edu). Digital Object Identifier 10.1109/TAC.2003.817010


  • Bounded real lemma
  • Discrete-time
  • H norm, Markovian jump linear systems (MJLSs)


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