Mathematics of Control, Signals and Systems

, Volume 1, Issue 3, pp 203–226 | Cite as

Persistency of excitation criteria for linear, multivariable, time-varying systems

  • I. M. Y. Mareels
  • M. Gevers


For continuous-time, multiple-input, multiple-output, linear systems, we present conditions under which the persistency of excitation of one regression vector implies the persistency of another regression vector derived from the first via a linear, dynamical transformation. We then introduce a definition of sufficient richness for vector input signals in the form of a persistency of excitation condition on a basis regression vector. Finally we establish input conditions which guarantee the persistency of excitation of a large class of regression vectors obtained from both time-invariant and time-varying systems.

Key words

Persistency of excitation System identification Adaptive control 


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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • I. M. Y. Mareels
    • 1
  • M. Gevers
    • 2
  1. 1.Laboratorium voor RegeltechniekRijksuniversiteit GentGentBelgium
  2. 2.Laboratoire d’Automatique, de Dynamique et d’Analyse des SystèmesUniversité de Louvain La NeuveLouvain La NeuveBelgium

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