中文摘要：

在界定了双线性系统、矩阵系统和右不变系统后，归纳出已有的3种不同系统的可控性定理。重点放在对右不变系统的可控性定理的总结以及与双线性系统可控性之间的关系上，特别强调了它们的可控性定理主要是根据李群、李代数的特性来判断的，以类似方法详细分析各种不同情况下的量子系统的可控性定理，通过对比，指出现有的有关量子系统可控性定理与双线性系统可控性定理之间的对应关系，由此揭示每一种量子系统可控性定理的适用情况以及各种不同量子系统可控性概念之间的相互关系。

英文摘要：

Bilinear systems, matrix systems and right-invariant systems are distinguished first. Then controllability theorems of such three different systems are summarized, the key points focus on the necessary and sufficient controllability conditions for right-invariant systems, and the relation with bilinear systems. Controllability theorems of these three different systems are especially emphasized by using Lie groups and Lie algebra. Different controllability theorems of quantum systems using similar method are analyzed in detail. Corresponding relations of controllability between quantum systems with bilinear systems are pointed out by means of comparison, and each type of controllability applied to different situations are also given. Relationships among different notions of controllability of quantum systems are established.