IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i17p2158-d628968.html
   My bibliography  Save this article

Arbitrary Coefficient Assignment by Static Output Feedback for Linear Differential Equations with Non-Commensurate Lumped and Distributed Delays

Author

Listed:
  • Vasilii Zaitsev

    (Laboratory of Mathematical Control Theory, Udmurt State University, 426034 Izhevsk, Russia
    These authors contributed equally to this work.)

  • Inna Kim

    (Laboratory of Mathematical Control Theory, Udmurt State University, 426034 Izhevsk, Russia
    These authors contributed equally to this work.)

Abstract

We consider a linear control system defined by a scalar stationary linear differential equation in the real or complex space with multiple non-commensurate lumped and distributed delays in the state. In the system, the input is a linear combination of multiple variables and its derivatives, and the output is a multidimensional vector of linear combinations of the state and its derivatives. For this system, we study the problem of arbitrary coefficient assignment for the characteristic function by linear static output feedback with lumped and distributed delays. We obtain necessary and sufficient conditions for the solvability of the arbitrary coefficient assignment problem by the static output feedback controller. Corollaries on arbitrary finite spectrum assignment and on stabilization of the system are obtained. We provide an example illustrating our results.

Suggested Citation

  • Vasilii Zaitsev & Inna Kim, 2021. "Arbitrary Coefficient Assignment by Static Output Feedback for Linear Differential Equations with Non-Commensurate Lumped and Distributed Delays," Mathematics, MDPI, vol. 9(17), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2158-:d:628968
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/17/2158/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/17/2158/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rosenthal, J. & Schumacher, J.M. & Willems, J.C., 1995. "Generic eigenvalue assignment by memoryless real output feedback," Other publications TiSEM 971c0413-f039-4eca-91a3-0, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. J. Leventides & N. Karcanias, 1998. "Dynamic Pole Assignment Using Global, Blow Up Linearization: Low Complexity Solutions," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 57-86, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2158-:d:628968. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.