Equivalence of nonlinear systems to triangular form: the singular case

S. Celikovsky, Sergej Celikovsky, Henk Nijmeijer

    Research output: Contribution to journalArticleAcademicpeer-review

    47 Citations (Scopus)
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    Abstract

    The problem of state equivalence of a given nonlinear system to a triangular form is considered here. The solution of this problem has been known for the regular case, i.e. when there exists a certain nested sequence of regular and involutive distributions. It is also known that in this case the corresponding system is linearizable using a smooth coordinate change and static state feedback. This paper deals with the singular case, i.e. when the nested sequence of involutive distributions of the system contains singular distributions. Special attention is paid to the so-called bijective triangular form. Geometric, coordinates-free criteria for the solution of the above problem as well as constructive, verifiable procedures are given. These results are used to obtain a result in the nonsmooth stabilization problem.
    Original languageUndefined
    Pages (from-to)135-144
    Number of pages10
    JournalSystems and control letters
    Volume27
    Issue number27
    DOIs
    Publication statusPublished - 1996

    Keywords

    • METIS-140858
    • IR-30218

    Cite this

    Celikovsky, S. ; Celikovsky, Sergej ; Nijmeijer, Henk. / Equivalence of nonlinear systems to triangular form: the singular case. In: Systems and control letters. 1996 ; Vol. 27, No. 27. pp. 135-144.
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    Equivalence of nonlinear systems to triangular form: the singular case. / Celikovsky, S.; Celikovsky, Sergej; Nijmeijer, Henk.

    In: Systems and control letters, Vol. 27, No. 27, 1996, p. 135-144.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Equivalence of nonlinear systems to triangular form: the singular case

    AU - Celikovsky, S.

    AU - Celikovsky, Sergej

    AU - Nijmeijer, Henk

    PY - 1996

    Y1 - 1996

    N2 - The problem of state equivalence of a given nonlinear system to a triangular form is considered here. The solution of this problem has been known for the regular case, i.e. when there exists a certain nested sequence of regular and involutive distributions. It is also known that in this case the corresponding system is linearizable using a smooth coordinate change and static state feedback. This paper deals with the singular case, i.e. when the nested sequence of involutive distributions of the system contains singular distributions. Special attention is paid to the so-called bijective triangular form. Geometric, coordinates-free criteria for the solution of the above problem as well as constructive, verifiable procedures are given. These results are used to obtain a result in the nonsmooth stabilization problem.

    AB - The problem of state equivalence of a given nonlinear system to a triangular form is considered here. The solution of this problem has been known for the regular case, i.e. when there exists a certain nested sequence of regular and involutive distributions. It is also known that in this case the corresponding system is linearizable using a smooth coordinate change and static state feedback. This paper deals with the singular case, i.e. when the nested sequence of involutive distributions of the system contains singular distributions. Special attention is paid to the so-called bijective triangular form. Geometric, coordinates-free criteria for the solution of the above problem as well as constructive, verifiable procedures are given. These results are used to obtain a result in the nonsmooth stabilization problem.

    KW - METIS-140858

    KW - IR-30218

    U2 - 10.1016/0167-6911(95)00059-3

    DO - 10.1016/0167-6911(95)00059-3

    M3 - Article

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    SP - 135

    EP - 144

    JO - Systems and control letters

    JF - Systems and control letters

    SN - 0167-6911

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