一、原理介绍：

http://s12/middle/84024a4a07aeb89c6f04b&690

http://s5/middle/84024a4a4cd3361ed1a04&690

二、实例解析

http://s14/middle/84024a4a07aeb89cb78fd&690

源代码：

clear all
close all
clc

T = 0.2;

%求解特征方程的系数alpha，这里用矩阵A表示
H = [0 0.196 0.443 0.624;0.196 0.443 0.624 0.748;0.443 0.624 0.748 0.831];
H1 = H(:,2:4);
H2 = 0 - H(:,1);

A = H1\H2;

%求解S
P = [A(3) A(2) A(1) 1];
X = roots(P);
S = log(X)/T

%求解C
B = [1 1 1;X(1) X(2) X(3);X(1)^2 X(2)^2 X(3)^2];
K = [0 0.196 0.443]';
C = B\K

运行结果：

得到结果如下：

S =

-0.0633

-1.7846

-11.1860

C =

1.1249

-1.3399

0.2150

则可知系统的传递函数为

http://s11/middle/84024a4a07aeb89c8d44a&690