分段线性状态延迟系统的可控性

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-01-10 DOI:10.1016/j.amc.2025.129281

Huiping Luo , JinRong Wang

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引用次数: 0

摘要

本文研究了分段线性状态延迟系统的可控性。为此，我们引入了一系列新函数，并给出了解的显式表示。然后，利用分段延迟Gramian矩阵建立了PLSDSs可控性的Gramian准则和秩准则。此外，所有驱动解从初始函数到期望的最终状态的控制函数都是通过移位的勒让德多项式来表征的。此外，还分别讨论了约束在不变子空间和弱非线性分段系统中的PLSDSs的可控性。数值算例验证了理论结果的有效性。

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Controllability of piecewise linear state-delay systems

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.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.