IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v481y2024ics0096300324003850.html
   My bibliography  Save this article

A Gramian matrix approach to synthesizing finite-frequency H2 controller

Author

Listed:
  • Quan, Hongzheng
  • Lu, Xiujuan
  • Cai, Chenxiao
  • Zou, Yun
  • Lam, James

Abstract

This paper studies the H2 control problem for linear continuous-time systems over a finite-frequency range. Using the finite-frequency Gramian matrix approach, a necessary and sufficient condition is obtained for the characterization of the finite-frequency H2 performance of a Hurwitz stability system. With such a characterization, a sufficient condition for the solvability of the finite-frequency H2 control problem is derived. An iterative algorithm is then constructed to solve the corresponding controller gain numerically. Finally, a numerical example of a two-cart-one-spring system is given to illustrate the effectiveness of the proposed scheme.

Suggested Citation

  • Quan, Hongzheng & Lu, Xiujuan & Cai, Chenxiao & Zou, Yun & Lam, James, 2024. "A Gramian matrix approach to synthesizing finite-frequency H2 controller," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    • Handle: RePEc:eee:apmaco:v:481:y:2024:i:c:s0096300324003850
    DOI: 10.1016/j.amc.2024.128924
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324003850
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.128924?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. Daraghmeh, Adnan & Hartmann, Carsten & Qatanani, Naji, 2019. "Balanced model reduction of linear systems with nonzero initial conditions: Singular perturbation approximation," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 295-307.
    2. Zhao, Younan & Gu, Peng & Zhu, Fanglai & Liu, Tianyi & Shen, Runjie, 2023. "Security control scheme for cyber-physical system with a complex network in physical layer against false data injection attacks," Applied Mathematics and Computation, Elsevier, vol. 447(C).
    3. Oliveira, Pedro M. & Palma, Jonathan M. & Lacerda, Márcio J., 2022. "H2 state-feedback control for discrete-time cyber-physical uncertain systems under DoS attacks," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    4. Ren, Yingying & Ding, Da-Wei & Long, Yue, 2023. "Finite-frequency fixed-order dynamic output-feedback control via a homogeneous polynomially parameter-dependent technique," Applied Mathematics and Computation, Elsevier, vol. 441(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. Li, Xin & Lei, Anzhi & Zhu, Liangkuan & Ban, Mingfei, 2024. "Improving Kalman filter for cyber physical systems subject to replay attacks: An attack-detection-based compensation strategy," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    2. Xian Xi & Xiangyun Gao & Xiaotian Sun & Huiling Zheng & Congcong Wu, 2024. "Dynamic analysis and application of network structure control in risk conduction in the industrial chain," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-13, December.
    3. Li, Yanpeng & Jiang, Yaolin & Yang, Ping, 2022. "Model order reduction of port-Hamiltonian systems with inhomogeneous initial conditions via approximate finite-time Gramians," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    4. Becker, Simon & Hartmann, Carsten & Redmann, Martin & Richter, Lorenz, 2022. "Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 107-141.
    5. Huang, He & Xu, Jiawei & Wang, Jing & Chen, Xiangyong, 2024. "Reinforcement learning-based secure synchronization for two-time-scale complex dynamical networks with malicious attacks," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    6. Wang, Chen & Qi, Yiwen & Tang, Yiwen & Li, Xin & Ji, Ming, 2024. "Robust control with protected feedback information for switched systems under injection attacks," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    7. Chen, Tianrui & Fan, Zezhou & Wang, Wenhua & Li, Wenxue, 2024. "Practical stabilization of multi-links highly nonlinear Takagi-Sugeno fuzzy complex networks with Lévy noise based on aperiodically intermittent discrete-time observation control," Applied Mathematics and Computation, Elsevier, vol. 476(C).

    More about this item

    Keywords

    Continuous-time system; Finite-frequency; Gramian matrix; H2 control;
    All these keywords.

    JEL classification:

    • H2 - Public Economics - - Taxation, Subsidies, and Revenue

    Statistics

    Access and download statistics

    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:apmaco:v:481:y:2024:i:c:s0096300324003850. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.