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

Victor Ayala; Adriano Da Silva; Anderson F. P. Rojas

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arXiv · 2402.18269

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

Victor 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 $\R^2$ 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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Victor Ayala, Adriano Da Silva, Anderson F. P. Rojas. 2024-02-28. Control sets of linear control systems on $\R^2$. The real case. https://arxiv.org/abs/2402.18269

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