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% Example 3.36 
% 
% Design of a minimum-order observer 
% 
a=[0 1 0; 0 0 1; -6 -11 -6]; 
b=[0; 0; 1]; c=[1 0 0]; 
aaa=[a(1,1)]; aab=[a(1,2:3)]; 
aba=[a(2:3,1)]; abb=[a(2:3,2:3)]; 
ba=b(1,1); bb=b(2:3,1); 
 
% subsystem 
a1=abb; c1=aab; 
disp('The rank of observability matrix') 
ro=rank(obsv(a1,c1)) 
 
%Construct dual system 
ax=a1'; 
bx=c1'; 
p=[-2+2*sqrt(3)*i -2-2*sqrt(3)*i]; 
k=acker(ax,bx,p); 
% State observer gain 
ke=k'