$$\mathbb {R}^2$$ 上线性控制系统的控制集 .实际情况

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-07-29 DOI:10.1007/s00030-024-00987-8

Víctor Ayala, Adriano Da Silva, Anderson F. P. Rojas

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引用次数: 0

摘要

本文研究了当相关矩阵具有实特征值时，线性控制系统在 $\mathbb {R}^2$ 上的动力学行为。与复数情况不同的是，我们发现如果矩阵不可逆，控制零点相对于控制范围的位置会对这种动力学产生强烈干扰。在可逆情况下，我们明确构建了具有非空内部的唯一控制集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Control sets of linear control systems on $$\mathbb {R}^2$$ . The real case$

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Control sets of linear control systems on $$\mathbb {R}^2$$ . The real case

In this paper, we study the dynamical behavior of a linear control system on $\mathbb {R}^2$ when the associated matrix has real eigenvalues. Different from the complex case, we show that the position of the control zero relative to the control range can have a strong interference in such dynamics if the matrix is not invertible. In the invertible case, we explicitly construct the unique control set with a nonempty interior.

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Nonlinear Differential Equations and Applications (NoDEA)

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