电网络二阶齐次方程复根状态轨迹画法的证明

Testimonial of Compound Roots State Locus Drawing of Two Rank Equation of Eleclric Network

描述二阶线性齐次自治方程的解有几种方法 ,其中状态向量法中用轨迹描绘最为直观 ,清晰且形象化 ,易于判断网络的稳定性[5] 。在众多轨迹法中 ,用特征值、特征向量等概念来描绘轨迹最能体现系统的本质特性。本文介绍这种方法 ,并给出系统具有复根时状态轨迹画法的证明。

There are several methods describing the solution of two rank linear autonomous equations. Among those methods, the method of state curve is the most direct-visual, distinct and vivid one, and ease to judge the stability of the net. Among the state curve methods, by using the characteristic roots, characteristic vector can be mostly reflected the essence of the system. This method is introduced briefly and the testimonial of drawing method is presented when the equation has compound roots.