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

Abstract

This paper explicitly computes the unique control set $D$ with non-empty interior of a linear control system on ${\mathbb{R}}^2$, when the associated matrix has complex eigenvalues. It turns out that the closure of $D$ coincides with the the region delimited by a computable periodic orbit $\mathcal{O}$ of the system.