# Talk:Beginning with CVX

### From Wikimization

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or | or | ||

<pre>[ v_W ] = eig ( full ( W ) ) | <pre>[ v_W ] = eig ( full ( W ) ) | ||

+ | .... | ||

+ | 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_W ' * W * v_W >= Epsilon1 * eye ( 4 ); | v_W ' * W * v_W >= Epsilon1 * eye ( 4 ); |

## Revision as of 02:34, 5 February 2009

lamda_W=eig(full(W))

Some one tell to me to upload the article that I'm reading for all the people could read it. I didn't know how to upload it, so I scan it and upload like some images (jpg). If it's wrong just tell to me and I will move or re-upload like jpg. The images are pag1 to pag7.

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.

I'm at work so I can't programm now, I will do it later.

At the paper puts:

normalized eigenvectors: v_W. And

v_W ' * W * v_W >= Epsilon1

v_W its a matrix, and Epsilon1 I think its an escalar, so a good idea could be:

[ v_W ] = eig ( full ( W ) ) .... 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_W_1 ' * W * v_W_1 >= Epsilon1 v_W_2 ' * W * v_W_2 >= Epsilon1 v_W_3 ' * W * v_W_3 >= Epsilon1 v_W_4 ' * W * v_W_4 >= Epsilon1 ....

or

[ v_W ] = eig ( full ( W ) ) .... 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_W ' * W * v_W >= Epsilon1 * eye ( 4 ); ....

I haven't Matlab here so it could be horrible.

Thanks for the ideas it's great. Thank you very much :D.

I have an answer, how to calculate the normalized eigenvector.

Maybe?[v_W]=eig(full(W))/norm ....

I've changed Epsilon1, Epsilon2, they aren't a variable, I think they are constants.

I'm going to see how to initialice (I'm going to research in the references of my article (Cross fingers)

Thanks a lot again.

Here is the new code:

clear all; n=2; m=1; A_a=3*eye(2*n,2*n) B_a=4*eye(2*n,2*m) W=eye(4) R=(zeros(2,4)) 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=1; Epsilon2=1; if(lamda_W>=Epsilon1) if(lamda_H<=-Epsilon2) para=1 else para = 0 end else para =0 end %v_W=eig(W)/(abs(eig(W))) %v_W=eig(full(W))/abs(full(W))%%normalized eigenvector :| %v_H=eig(H)/max(eig(H)) while para==0 [v_W,D] = eig(W) [v_H,D] = eig(H) if ( Epsilon1 - lamda_W )>(lamda_H+Epsilon2) 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' W - Epsilon1*eye(2*n) == semidefinite(2*n); Epsilon2*eye(2*n) + H == -semidefinite(2*n); v_W'*W*v_W>=Epsilon1*eye(4) cvx_end else 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' W - Epsilon1*eye(2*n) == semidefinite(2*n); Epsilon2*eye(2*n) + H == -semidefinite(2*n); v_H'*H*v_H<=-Epsilon2*eye(4) cvx_end end lamda_W=min(eig(full(W))) lamda_H=max(eig(H)) % v_W=eig(full(W))/max(eig(full(W)))%%Cálculo del normalized eigenvector % v_H=eig(H)/max(eig(H)) %STOP if(lamda_W>=Epsilon1) if(lamda_H<=-Epsilon2) para=1 else para = 0 end else para =0 end end R W K=R/W