Lyapunov functions for the multivariable Popov criterion with indefinite multipliers

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Abstract

We demonstrate the existence of Lur'e-Postnikov type Lyapunov functions for a reasonably general form of the multivariable Popov criterion. In particular, the multipliers need not be positive semi-definite. We discuss the application to the special cases where the feedback element is either diagonal, unstructured or linear.
Original languageEnglish
Pages (from-to)2977-2981
Number of pages4
JournalAutomatica
Volume45
Issue number12
Early online date8 Oct 2009
DOIs
Publication statusPublished - 1 Dec 2009

Keywords

  • Lyapunov functions
  • Multipliers
  • Multivariable feedback systems
  • Popov criterion
  • Stability tests

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