Necessary conditions for stability and attractivity of continuous systems

R. Orsi*, L. Praly, I. Mareels

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    16 Citations (Scopus)

    Abstract

    Considered in this paper are control systems of the form ẋ = f(x, u). For such systems a number of related necessary conditions for various forms of stability and attractivity are presented. The paper starts by showing that Brockett's necessary condition for stabilizability via smooth feedback still persists if f is continuous and the class of allowable u increased to include continuous feedbacks. Using similar ideas to those used to prove the continuous Brockett result, again only assuming continuity of f and u, necessary conditions are then derived for global attractivity and for ultimate boundedness.

    Original languageEnglish
    Pages (from-to)1070-1077
    Number of pages8
    JournalInternational Journal of Control
    Volume76
    Issue number11
    DOIs
    Publication statusPublished - 20 Jul 2003

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