线性反馈控制系统的代数结构分析

Analysis of Algebraic Structures for Linear Feedback Control Systems

该文研究稳定连续控制系统的代数结构分析问题，旨在利用广义逆理论及矩阵分解技巧，给出线性连续系统的所有稳定化状态反馈控制器的参数化代数刻划，以及期望解存在的充要条件。结果表明，上述目的可通过求解一线性矩阵不等式而达到。文中给出了说明性的数值例子。该文结果为稳定控制系统的分析与设计提供了一种简单有效的新途径，因而具有较强的理论意义。与传统的几何方法相比，该文采用纯代数手段刻划的参数空间更易于工程实现。

This paper studies the problem of analyzing algebraic structures of stable linear continuous control systems. The problem addressed is to give the algebraic parametrization of all stabilizing state feedback controllers for linear continuous systems by using the generalized inverse theory and matris decomPOSition techntries, and to give the sufficient and necessary conditions for the existence of desired solutions. It is shown that the above goal can be achieved by solving a linear matrix unequality. An illustrative numerical example is also presented. The results obtained in this paper offer a simple and effective approach to the analysis and design of stable control systems, and therefore have gnd theoretical significance. Compared to the traditional gcometric method, the parameter space characterised by purely algebraic method in this paper is more suitable for englneering realization.