中文摘要：

研究了欧氏空间Rn上的线性系统和它的梯度扩张系统的能控性之间的关系以及它们的能观测性之间的关系,证明了线性系统的梯度扩张系统是能控的（或能观测的）当且仅当原线性系统既是能控的,又是能观测的。

英文摘要：

The relation between controllability of linear gradient extension system is studied. At the same time, systems on Euclidean space Rn and controllability of the relation between observability of linear systems and observability of gradient extension system is studied. It is proved that the gradient extension of linear system is controllable （or observable） if and only if the linear system is controllable and observable.