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% Example 3.19 
% 
num=[1 2]; 
den1=[1 4 3]; 
den=conv(den1,den1); 
figure(1) 
rlocus(num,den) 
title('Root Locus') 
[k,p]=rlocfind(num,den) 
 
%  Checking the stability 
figure(2) 
k=55; 
num1=k*[1 2]; 
den=[1 4 3]; 
den1=conv(den,den); 
[num,den]=cloop(num1,den1,-1); 
impulse(num,den) 
title('Impulse Response (k=55) ') 
 
%  Checking the stability 
figure(3) 
k=56; 
num1=k*[1 2]; 
den=[1 4 3]; 
den1=conv(den,den); 
[num,den]=cloop(num1,den1,-1); 
impulse(num,den) 
title('Impulse Response (k=56) ') 
 
 
 
% the result 
 
Select a point in the graphics window 
 
selected_point = 
      0.0000 - 3.1579i 
 
k = 
   55.6908 
p = 
  -5.9878 
   0.0029 + 3.1564i 
   0.0029 - 3.1564i 
  -2.0179