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    On the Dynamic Instability of a Class of Switching System


    Shorten, Robert N. and Ó Cairbre, Fiacre and Curran, Paul (2000) On the Dynamic Instability of a Class of Switching System. IFAC Proceedings Volumes, 33 (28). pp. 189-194. ISSN 1474-6670

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    Abstract

    A sufficient condition for the existence of a destabilising switching sequence for the system x = A(t)x, A(t) E {Al,A2 , ... ,AM}, Ai E lRNXN , where the Ai are Hurwitz matrices, is that there exists non-negative real constants 0'1,0'2, ... , O'M, O'j 2: 0, L:f'!1 0'; > 0, such that the matrix pencil L:f'! IO'jAj has at least one eigenvalue with a positive real part. An informal proof of this result based upon Floquet theory was presented in (Shorten, 1996; Shorten and Narendra, 1997) . In this paper we present a rigourous basis for the proof of this result. Further, we use this result to identify several classes of linear switching systems, which admit the existence of a destabilising switching sequence. These systems provide insights into the relationship between the existence of a common quadratic Lyapunov function and the existence of a destabilising switching sequence for low order systems, as well as the robustness of a class of switching system that is known to be exponentially stable.

    Item Type: Article
    Keywords: Stability Theory; Switching Systems; Hybrid Systems; Multiple Models;
    Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 10096
    Identification Number: https://doi.org/10.1016/S1474-6670(17)36832-5
    Depositing User: Dr. Fiacre O Cairbre
    Date Deposited: 15 Oct 2018 15:27
    Journal or Publication Title: IFAC Proceedings Volumes
    Publisher: Elsevier
    Refereed: Yes
    Funders: European Union Multi-Agent Control
    URI:

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