Razumikhin technique for stabilisation of highly nonlinear hybrid systems by bounded discrete-time state feedback control working intermittently

Xu, Henglei and Mao, Xuerong (2024) Razumikhin technique for stabilisation of highly nonlinear hybrid systems by bounded discrete-time state feedback control working intermittently. Numerical Algebra, Control and Optimization, 14 (4). pp. 669-687. (https://doi.org/10.3934/naco.2024003)

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Abstract

This paper applies the Razumikhin idea to study the stabilisation of hybrid stochastic systems by discrete-time state feedback control, which works intermittently and is designed boundedly. Theoretically, the Razumikhin method is generalised in view of time-varying functions, rather than constants, where the time-inhomogeneous property of intermittent control could be fully made use of. In practice, the control cost could be reduced significantly since the controller is bounded, not observed continuously and having rest time. Moreover, there will be a wider range of applications especially for models that do not satisfy the linear growth condition (say highly nonlinear). An example of the coupled Van der Pol–Duffing oscillator system is hence provided to show the practicability of the developed theory.

ORCID iDs

Xu, Henglei and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
  • Item type:Article
    ID code:88332
    Dates:
    Date
    Event
    1 December 2024
    Published
    31 January 2024
    Published Online
    17 January 2024
    Accepted
    Notes:Copyright © 2024 Owner. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Numerical Algebra, Control and Optimization following peer review. The definitive publisher-authenticated version (Xu, H & Mao, X 2024, 'Razumikhin technique for stabilisation of highly nonlinear hybrid systems by bounded discrete-time state feedback control working intermittently', Numerical Algebra, Control and Optimization) is available online at https://doi.org/10.3934/naco.2024003.
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:05 Mar 2024 11:25
    Last modified:21 Nov 2024 01:25
    URI:https://strathprints.strath.ac.uk/id/eprint/88332
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