In this paper, we study the dynamical behavior of a linear control system on 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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Ayala et al. (2024) studied this question.
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