A KYP lemma for LMI regions

Brandon Hencey, Andrew G. Alleyne

Research output: Contribution to journalArticlepeer-review


In this technical note, a Kalman-Yakubovich-Popov (KYP) lemma is discussed for linear matrix inequality (LMI) regions. Sufficient quadratic stability conditions are developed for an uncertain linear system subject to time varying uncertainty satisfying a quadratic inequality. Furthermore, the quadratic stability conditions are shown to guarantee the satisfaction of a frequency domain inequality.

Original languageEnglish (US)
Pages (from-to)1926-1930
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number10
StatePublished - Oct 2007


  • Kalman-Yakubovich-Popov (KYP) lemma
  • Linear matrix inequality (LMI)
  • Regional pole placement
  • Uncertainty

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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