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J
Posts:
9
Registered:
8/29/09


Re: LMI/Optimization problem with LMI toolbox
Posted:
Aug 29, 2009 12:32 PM


Peter
You can use the mincx function as long as you declare the 'k' variable along the lines of:
k=lmivar(1,[N_k,0]); % k*eye(N_k) X=lmivar(1,[N_x,1]);
Assume that you have delcared your two variables in this order and have an lmi system 'lmi_system'. Then construct a linear function of LMItoolbox's decvar's as follows:
n=decnbr(lmi_system); c=zeros(n,1); c(1)=1;
This should give 'k=c'*decvars'. Now use :
[kmin,xmin]=mincx(lmi_system,c);
J
"Peter R" <peter.rqeu@gmail.com> wrote in message <h5kjk1$dtl$1@fred.mathworks.com>... > Hi, > > I am trying to solve the following optimization problem (with constraint) in Matlab: > > minimize k ('k' is a scalar) > subject to the following LMI: > [X'*A+AX B; B' k*I]<0 > > where A, B, I are matrices (I being the identity matrix). > > I can formulate the LMI, [X'*A+AX B; B' k*I]<0, in Matlab using the LMItoolbox; however, I don't know how the minimization of 'k' is done. > Or perhaps I should ask how the function mincx() is written to achieve this. > > Any suggestion? > > Thanks, > P.


Date

Subject

Author

8/8/09


Peter R

8/29/09


J


