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Controllability of piecewise linear state-delay systems

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  • Luo, Huiping
  • Wang, JinRong

Abstract

In this paper, we study the controllability of piecewise linear state-delay systems (PLSDSs). To do this, we introduce a series of new functions and give the explicit representation of the solution. Then, the Gramian and the rank criteria for the controllability of PLSDSs are established by the piecewise delayed Gramian matrix. Further, all control functions driving the solution from an initial function to a desired final state are characterized by virtue of shifted Legendre polynomials. In addition, the controllability of PLSDSs constrained in an invariant subspace and weakly nonlinear piecewise systems are discussed as well, respectively. Numerical examples are provided to verify the effectiveness of theoretical results.

Suggested Citation

  • Luo, Huiping & Wang, JinRong, 2025. "Controllability of piecewise linear state-delay systems," Applied Mathematics and Computation, Elsevier, vol. 494(C).
    • Handle: RePEc:eee:apmaco:v:494:y:2025:i:c:s0096300325000086
    DOI: 10.1016/j.amc.2025.129281
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    References listed on IDEAS

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    1. Kumar, Vipin & Stamov, Gani & Stamova, Ivanka, 2023. "Controllability Results for a Class of Piecewise Nonlinear Impulsive Fractional Dynamic Systems," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    2. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    3. Vadivoo, B.S. & Jothilakshmi, G. & Almalki, Y. & Debbouche, A. & Lavanya, M., 2022. "Relative controllability analysis of fractional order differential equations with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 428(C).
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