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Lmi matlab toolbox.

A=[-1 -2 1; 3 2 1; 1 -2 -1;];
B=[1 0 1]'
E1=[-1 -2 1; 1 3 2; 2 -2 -1;];
E2=[0 0 1]';
D=[0 0 1]';
setlmis([]) 
Q=lmivar(1,[3 1])%3x3 symmetric matrix
Y= lmivar(2,[1 3])%1x3 matrix

% 1st LMI 
lmiterm([1 1 1 Q],1,A,'s')%A*Q+Q*A' 
lmiterm([1 1 1 Y],-1,B,'s')%_B*Y-(B*Y)'
lmiterm([1 1 1 0],D*D')%D*D'

lmiterm([1 2 1 Q],1,E1)%E1*Q
lmiterm([1 2 1 Y],-1,E2)%-E2*Y

lmiterm([1 2 2 0],-1)%-gamma^2*I<-----how to put gamma also.

% 2nd LMI 
lmiterm([-2 1 1 Q],1,1)%Q>0<-------?

LMISYS = getlmis
gamma1=mat2dec(LMISYS,Q,Y)
options = [1e-5,0,0,0,0];
[gamma1opt,qopt]=mincx(LMISYS,gamma1,options)
[gamma1opt,yopt]=mincx(LMISYS,gamma1,options)
Qopt = dec2mat(LMISYS,qopt,Q)
Yopt = dec2mat(LMISYS,yopt,Y)

I have to minimize gamma, and to find matrices Q and Y. I am getting errors. I do not if the code is correct. The matrix inequality is: M=[A*Q+Q*A'-B*Y-Y'*B'+D*D' (E1*Q-E2*Y)'; E1*Q-E2*Y -gamma^2*eye(3);]
Thanks In advance.
0
6/30/2011 11:25:05 PM
comp.soft-sys.matlab 211264 articles. 26 followers. lunamoonmoon (257) is leader. Post Follow

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Same answer here as on your YALMIP question.

"tho" wrote in message <iuj0kg$sln$1@newscl01ah.mathworks.com>...
> A=[-1 -2 1; 3 2 1; 1 -2 -1;];
> B=[1 0 1]'
> E1=[-1 -2 1; 1 3 2; 2 -2 -1;];
> E2=[0 0 1]';
> D=[0 0 1]';
> setlmis([]) 
> Q=lmivar(1,[3 1])%3x3 symmetric matrix
> Y= lmivar(2,[1 3])%1x3 matrix
> 
> % 1st LMI 
> lmiterm([1 1 1 Q],1,A,'s')%A*Q+Q*A' 
> lmiterm([1 1 1 Y],-1,B,'s')%_B*Y-(B*Y)'
> lmiterm([1 1 1 0],D*D')%D*D'
> 
> lmiterm([1 2 1 Q],1,E1)%E1*Q
> lmiterm([1 2 1 Y],-1,E2)%-E2*Y
> 
> lmiterm([1 2 2 0],-1)%-gamma^2*I<-----how to put gamma also.
> 
> % 2nd LMI 
> lmiterm([-2 1 1 Q],1,1)%Q>0<-------?
> 
> LMISYS = getlmis
> gamma1=mat2dec(LMISYS,Q,Y)
> options = [1e-5,0,0,0,0];
> [gamma1opt,qopt]=mincx(LMISYS,gamma1,options)
> [gamma1opt,yopt]=mincx(LMISYS,gamma1,options)
> Qopt = dec2mat(LMISYS,qopt,Q)
> Yopt = dec2mat(LMISYS,yopt,Y)
> 
> I have to minimize gamma, and to find matrices Q and Y. I am getting errors. I do not if the code is correct. The matrix inequality is: M=[A*Q+Q*A'-B*Y-Y'*B'+D*D' (E1*Q-E2*Y)'; E1*Q-E2*Y -gamma^2*eye(3);]
> Thanks In advance.
0
johanl (31)
7/1/2011 5:50:25 AM
"Johan Löfberg" wrote in message <iujn71$m6q$1@newscl01ah.mathworks.com>...
Yes, I just wanted to know how this is being solved using the lmi matlab toolbox, because I heard that it gives more stable results.
> Same answer here as on your YALMIP question.
> 
> "tho" wrote in message <iuj0kg$sln$1@newscl01ah.mathworks.com>...
> > A=[-1 -2 1; 3 2 1; 1 -2 -1;];
> > B=[1 0 1]'
> > E1=[-1 -2 1; 1 3 2; 2 -2 -1;];
> > E2=[0 0 1]';
> > D=[0 0 1]';
> > setlmis([]) 
> > Q=lmivar(1,[3 1])%3x3 symmetric matrix
> > Y= lmivar(2,[1 3])%1x3 matrix
> > 
> > % 1st LMI 
> > lmiterm([1 1 1 Q],1,A,'s')%A*Q+Q*A' 
> > lmiterm([1 1 1 Y],-1,B,'s')%_B*Y-(B*Y)'
> > lmiterm([1 1 1 0],D*D')%D*D'
> > 
> > lmiterm([1 2 1 Q],1,E1)%E1*Q
> > lmiterm([1 2 1 Y],-1,E2)%-E2*Y
> > 
> > lmiterm([1 2 2 0],-1)%-gamma^2*I<-----how to put gamma also.
> > 
> > % 2nd LMI 
> > lmiterm([-2 1 1 Q],1,1)%Q>0<-------?
> > 
> > LMISYS = getlmis
> > gamma1=mat2dec(LMISYS,Q,Y)
> > options = [1e-5,0,0,0,0];
> > [gamma1opt,qopt]=mincx(LMISYS,gamma1,options)
> > [gamma1opt,yopt]=mincx(LMISYS,gamma1,options)
> > Qopt = dec2mat(LMISYS,qopt,Q)
> > Yopt = dec2mat(LMISYS,yopt,Y)
> > 
> > I have to minimize gamma, and to find matrices Q and Y. I am getting errors. I do not if the code is correct. The matrix inequality is: M=[A*Q+Q*A'-B*Y-Y'*B'+D*D' (E1*Q-E2*Y)'; E1*Q-E2*Y -gamma^2*eye(3);]
> > Thanks In advance.
0
7/1/2011 11:15:13 AM
Reply:

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