In this paper we study the main properties of control sets with nonempty interior of linear control systems on semisimple Lie groups. We show that, unlike the solvable case, linear control systems on semisimple Lie groups may have more than one control set with nonempty interior and that they are contained in right translations of the one around the identity.

中文翻译：

---

半单李群上的线性系统控制集

在本文中，我们研究了半单李群上线性控制系统具有非空内部控制集的主要性质。我们表明，与可解情况不同，半单李群上的线性控制系统可能具有多个内部非空的控制集，并且它们包含在恒等式的正确翻译中。