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% Example 3.42 
% 
% Design of state observer 
% 
g=[0 0 1; 1 0 0; -0.2 -0.5 1.1]; 
h=[0; 0; 1]; c=[1 0 0]; 
% Check the controllability and observability 
disp('The rank of controllability matrix') 
rc=rank(ctrb(g,h)) 
disp('The rank of observability matrix') 
ro=rank(obsv(g,c)) 
 
% Design Digital controller 
p=[0 0 0]; 
k=acker(g,h,p) 
 
% Design state observer 
gaa=g(1,1); gab=g(1,2:3); 
gba=g(2:3,1); gbb=g(2:3,2:3); 
ha=h(1,1); hb=h(2:3,1); 
 % Dual system 
g1=gbb'; h1=gab'; 
p=[0 0]; 
k=acker(g1,h1,p); 
ke=k'