A note on persistency of excitation

JC Willems, P Rapisarda, Markovsky*, BLM De Moor

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    219 Citations (Web of Science)


    We prove that if a component of the response signal of a controllable linear time-invariant system is persistently exciting of sufficiently high order, then the windows of the signal span the full system behavior. This is then applied to obtain conditions under which the state trajectory of a state representation spans the whole state space. The related question of when the matrix formed from a state sequence has linearly independent rows from the matrix formed from an input sequence and a finite number of its shifts is of central importance in subspace system identification. (C) 2004 Elsevier B.V. All rights reserved.

    Original languageEnglish
    Pages (from-to)325-329
    Number of pages5
    JournalSystems & Control Letters
    Issue number4
    Publication statusPublished - Apr 2005


    • bahavioral systems
    • persistency of excitation
    • lags
    • annihilators
    • system identification

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