Controllability of piecewise linear state-delay systems

被引：0

作者：

Luo, Huiping ^{[1
,2
]}

Wang, Jinrong ^{[1
,2
]}

机构：

[1] Guizhou Univ, Sch Math & Stat, Guiyang 550025, Guizhou, Peoples R China

[2] Guizhou Univ, Supercomp Algorithm & Applicat Lab, Guian Sci Innovat Co, Guiyang 550025, Guizhou, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2025年 / 494卷

基金：

中国国家自然科学基金;

关键词：

Controllability; Piecewise system; State-delay; Control function; Shifted Legendre polynomial; NEUTRAL DIFFERENTIAL-EQUATIONS; FINITE-TIME STABILITY; RELATIVE-CONTROLLABILITY; INPUT;

D O I：

10.1016/j.amc.2025.129281

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：22

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