Article

New relationships between Lyapunov functions and the passivity theorem

  1. B. Brogliato1,†,
  2. R. Lozano2,†,
  3. I. D. Landau3,†

Article first published online: 21 MAR 2007

DOI: 10.1002/acs.4480070505

Issue

International Journal of Adaptive Control and Signal Processing

International Journal of Adaptive Control and Signal Processing

Volume 7, Issue 5, pages 353–365, September 1993

Additional Information

How to Cite

Brogliato, B., Lozano, R. and Landau, I. D. (1993), New relationships between Lyapunov functions and the passivity theorem. Int. J. Adapt. Control Signal Process., 7: 353–365. doi: 10.1002/acs.4480070505

Author Information

  1. 1

    Laboratoire d'Automatigue de Grenoble, URA CNRS 228. BP 46, Saint Martin d'Hères, France

  2. 2

    Université de Technologie de Compiègne, Heudiasyc URA CNRS 817, Centre de Recherches de Royallieu, BP 233. F-60206 Compiègne Cedex, France

  3. 3

    Laboratoire d'Automatique de Grenoble, URA CNRS 228, BP 46, Saint Martin d'ères, France

  1. †

    All authors are also members of the Groupement de Recherches en Automatique, CNRS.

Publication History

  1. Issue published online: 21 MAR 2007
  2. Article first published online: 21 MAR 2007

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Keywords:

  • Lyapunov functions;
  • Passivity theorem;
  • Adaptive control

Abstract

In this paper we study new relationships between a class of Lyapunov functions and the passivity theorem. It is proved that under some (sufficient) conditions a Lyapunov-stable system can be analysed as the feedback connection of two (strictly) passive subsystems. It is also shown that very recent adaptive schemes for linear plants of any relative degree can in a certain sense be unified through a passivity point of view.

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