IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i2p202-d317262.html
   My bibliography  Save this article

Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities

Author

Listed:
  • Angelo Alessandri

    (The Department of Mechanical, Energetics, Management, and Transportation Engineering (DIME), University of Genoa, Via Opera Pia 15, 16145 Genoa, Italy)

Abstract

Lyapunov functions enable analyzing the stability of dynamic systems described by ordinary differential equations without finding the solution of such equations. For nonlinear systems, devising a Lyapunov function is not an easy task to solve in general. In this paper, we present an approach to the construction of Lyapunov funtions to prove stability in estimation problems. To this end, we motivate the adoption of input-to-state stability (ISS) to deal with the estimation error involved by state observers in performing state estimation for nonlinear continuous-time systems. Such stability properties are ensured by means of ISS Lyapunov functions that satisfy Hamilton–Jacobi inequalities. Based on this general framework, we focus on observers for polynomial nonlinear systems and the sum-of-squares paradigm to find such Lyapunov functions.

Suggested Citation

  • Angelo Alessandri, 2020. "Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:202-:d:317262
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/2/202/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/2/202/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bin Liu & Bo Xu & Guohua Zhang & Lisheng Tong, 2019. "Review of Some Control Theory Results on Uniform Stability of Impulsive Systems," Mathematics, MDPI, vol. 7(12), pages 1-28, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Artun Sel & Bilgehan Sel & Umit Coskun & Cosku Kasnakoglu, 2022. "SOS-Based Nonlinear Observer Design for Simultaneous State and Disturbance Estimation Designed for a PMSM Model," Sustainability, MDPI, vol. 14(17), pages 1-12, August.

    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. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    2. Daniel Ríos-Rivera & Alma Y. Alanis & Edgar N. Sanchez, 2020. "Neural-Impulsive Pinning Control for Complex Networks Based on V-Stability," Mathematics, MDPI, vol. 8(9), pages 1-20, August.

    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:8:y:2020:i:2:p:202-:d:317262. 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.