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

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

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.

Abstract Image

$$\mathbb {R}^2$$ 上线性控制系统的控制集 .实际情况
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。
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