IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v175y2023ip2s0960077923009530.html
   My bibliography  Save this article

Autonomous second-order nonlinear systems and weighted linearization: Under what conditions are the inherent specifications preserved?

Author

Listed:
  • Tavazoei, Mohammad Saleh

Abstract

Recently, an interesting idea on generalizing the traditional linearization technique by weighting integration of the Jacobian matrix over the state space has been introduced, and its usefulness has been verified in control system design. Noticing the applicability of linearized models in studying the properties of original systems in the literature relevant to nonlinear systems, this paper aims to investigate the aforementioned generalized linearization technique in the viewpoint of preserving the specifications of an autonomous second-order nonlinear system. To this end, by considering a general form for the weight function possessing two adjustable parameters, the regions in the space of tunable parameters of weight function in which the linearized model preserves the specifications of the original nonlinear system are analytically specified. The specifications, whose preservation is investigated, include stability/instability status of the system equilibrium point, the type of this equilibrium point, eigenvalue location of the corresponding Jacobian matrix, and quadratic Lyapunov function corresponding to a stable equilibrium point. The analytical achievements of the paper are verified by various numerical examples.

Suggested Citation

  • Tavazoei, Mohammad Saleh, 2023. "Autonomous second-order nonlinear systems and weighted linearization: Under what conditions are the inherent specifications preserved?," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p2:s0960077923009530
    DOI: 10.1016/j.chaos.2023.114052
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923009530
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114052?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Khan, Muhammad Bilal & Othman, Hakeem A. & Santos-García, Gustavo & Saeed, Tareq & Soliman, Mohamed S., 2023. "On fuzzy fractional integral operators having exponential kernels and related certain inequalities for exponential trigonometric convex fuzzy-number valued mappings," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Llibre, Jaume & Salhi, Tayeb, 2022. "On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    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. Muhammad Bilal Khan & Ali Althobaiti & Cheng-Chi Lee & Mohamed S. Soliman & Chun-Ta Li, 2023. "Some New Properties of Convex Fuzzy-Number-Valued Mappings on Coordinates Using Up and Down Fuzzy Relations and Related Inequalities," Mathematics, MDPI, vol. 11(13), pages 1-23, June.
    2. Mesfer H. Alqahtani & Der-Chyuan Lou & Fahad Sikander & Yaser Saber & Cheng-Chi Lee, 2024. "Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals," Mathematics, MDPI, vol. 12(22), pages 1-29, November.

    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:eee:chsofr:v:175:y:2023:i:p2:s0960077923009530. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.