Talk:Beginning with CVX

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</pre>
</pre>
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The paper its: Pole assignment of linear uncertain systems in a sector via a lyapunov - tipe approach. D. Arzeiler, J. Bernussou and G. Garcia. IEEE transactions automatic control, vol 38, nº 7, July 1993.
 
Thanks a lot for all the ideas, they all are greats.
Thanks a lot for all the ideas, they all are greats.
-
I don't know how to initialice Epsilon1 and Epsilon2 I'm going to research in the references of my article (Cross fingers)
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I don't know how to initialice Epsilon1 and Epsilon2. At the article don't put anything.
 +
 
 +
I put off the while structure.
Thanks a lot again.
Thanks a lot again.
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Here is the new code:
Here is the new code:
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<pre>
+
<pre>%0)Initialization
-
%0)Initialization
+
clear all;
clear all;
n=2; m=1;
n=2; m=1;
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end
end
 +
%while para==0
%3)3
%3)3
[v_W,D] = eig( full ( W ) )
[v_W,D] = eig( full ( W ) )
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end
end
-
lamda_W = min ( eig ( full ( W ) ) )
 
-
lamda_H = max ( eig ( full ( H ) ) )
 
R
R
W=full(W)
W=full(W)
K=R/W
K=R/W
- 
</pre>
</pre>

Revision as of 11:02, 5 February 2009

lamda_W=eig(full(W))

Thanks a lot for all the ideas, they all are greats.

I don't know how to initialice Epsilon1 and Epsilon2. At the article don't put anything.

I put off the while structure.

Thanks a lot again.

Here is the new code: 

%0)Initialization
clear all;
n=2; m=1;

A_a=3*eye(2*n,2*n)
B_a=4*eye(2*n,2*m) 

%1)1
W=eye(4)
R=(zeros(2,4))

%2)2
H=W*A_a'+A_a*W-B_a*R-R'*B_a'

lamda_W=min(eig(full(W)))
lamda_H=max(eig(H))

Epsilon1=11;
Epsilon2=0.1;

if(lamda_W>=Epsilon1)
    if(lamda_H<=-Epsilon2)     para=1
    else para = 0
    end
else para =0
end

%while para==0
    %3)3
    [v_W,D] = eig( full ( W ) )
    [v_H,D] = eig( full ( H ) )
    
    v_W_1 = v_W( : , 1 ) / norm ( v_W ( : , 1 ) ) ;
    v_W_2 = v_W( : , 2 ) / norm ( v_W ( : , 2 ) ) ;
    v_W_3 = v_W( : , 3 ) / norm ( v_W ( : , 3 ) ) ;
    v_W_4 = v_W( : , 4 ) / norm ( v_W ( : , 4 ) ) ;
    
    v_H_1 = v_H( : , 1 ) / norm ( v_H ( : , 1 ) ) ;
    v_H_2 = v_H( : , 2 ) / norm ( v_H ( : , 2 ) ) ;
    v_H_3 = v_H( : , 3 ) / norm ( v_H ( : , 3 ) ) ;
    v_H_4 = v_H( : , 4 ) / norm ( v_H ( : , 4 ) ) ;

    %4a)4a
if ( Epsilon1 - lamda_W )>(lamda_H+Epsilon2)
    Caso=1 %For know where am I

    cvx_begin
    variables p1 p2 W(4,4) R(2,4)
    
    minimize (p1+p2)
    
    subject to

        W(1,1)<=p1
        W(2,2)<=p1
        W(1,1)>=Epsilon1
        W(2,2)>=Epsilon1
        W(3,3)==W(1,1)
        W(4,4)==W(2,2)

        R(1,1)>=-p2
        R(1,1)<=p2
        R(2,3)==R(1,1)
        R(1,2)>=-p2
        R(1,2)<=p2
        R(2,4)==R(1,2)
     
        H=W*A_a'+A_a*W-B_a*R-R'*B_a'
        
        v_W'*W*v_W - Epsilon1*eye(2*n) == semidefinite(2*n);

cvx_end

else %4b)4b

    Caso = 2
    cvx_begin
    
    variables p1 p2 W(4,4) R(2,4)
    
    minimize (p1+p2)
    
    subject to
        
        W(1,1)>=Epsilon1
        W(2,2)>=Epsilon1
        W(1,1)<=p1
        W(2,2)<=p1
        W(3,3)==W(1,1)
        W(4,4)==W(2,2)

        R(1,1)>=-p2
        R(1,1)<=p2
        R(2,3)==R(1,1)
        R(1,2)>=-p2
        R(1,2)<=p2
        R(2,4)==R(1,2)

        H=W*A_a'+A_a*W-B_a*R-R'*B_a'
        
        Epsilon2*eye(2*n) + v_H'*H*v_H == -semidefinite(2*n);        

cvx_end
end


R
W=full(W)
K=R/W
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