控制燃料受限下离散线性系统能控域的研究

A Study of the Controllable Region for the Discrete-Time Linear System with the Constraint of the Control Fuel

本文讨论控制燃料受限下离散线性系统能控域问题。文中籍助于矩量论方法与线性系统分解技巧得到了能控域的结构性定理,该定理除与系统的Jordan分解有关外,还与状态矩阵的特征值有关。此外,文中还给出了判别任给状态是否属于能控域的显式判别条件。这些结果在实际应用中是有用的。

In this paper,we discusses the problem of the controllable region for the discrete-time linear system with the constraint of the control fuel.The theorem of the structure of the controllable region is obtained by using the method of the moment theory and the decomposition technique of the linear system.This theorem is not only concerned with the Jordan decomposition of the linear system,but is also associated with the eigenvalue of the state matrix.Besides,in this paper we also give an explicit condition which can be used to judge whether an arbitrary given state is in the controllable region.All these results may be useful in the practical application.