一个常系数线性动态系统稳定性的判别法则

A Criterion on Linear System Stability

本文通过将常系数动态系统状态矩阵分解为一个对称矩阵和一个反对称矩阵.进而找出这两个分解矩阵的特征值与原状态矩阵特征值的依赖关系的方法,导出一个十分简单的判定线性常系数动态系统稳定性的法则。

A simple method of calculating stability conditions for a linear system is given by means of separating state matrix. In this paper state matrix is separated into a symmetry matrix Ad and a unsymmetry matrix Af and furter-more the relation between the eigenvalues of the matrix Ad and the eigenvalues of the matrix Af is found. Finally a criterion of determining stability for a linear system is deduced by calculating the eigenvalues of the matrix Ad or by deciding if the matrix Ad is strictly negtive.