线性系统Hamilton扩张系统的能控性和能观测性

Controllability and Observability of Hamilton Extension of a Linear System

利用控制系统的微分几何理论,研究了线性系统和它的Hamilton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。通过计算线性系统的能控性矩阵和它的Hamilton扩张系统的能控性矩阵,证明了线性系统和它的Hamilton扩张系统的能控性是等价的。同时通过计算线性系统的能观测性矩阵和它的Hamilton扩张系统的能观测性矩阵,证明了线性系统和它的Hamilton扩张系统的能观测性也是等价的。证明了线性系统的Hamilton扩张系统是能控的当且仅当它是能观测的,原线性系统既是能控的,又是能观测的。

The relationship between controllability of linear systems and controllability of Hamilton extension system is studied by using differential geometry theory of control systems.At the same time,the equivalence between controllability of linear systems and controllability of Hamilton extension system is proved by controllability matrix.It is proved that the Hamilton extension of linear system is controllable if and only if it is observable,if and only if the linear system is controllable and observable.