Math Forum Discussions

J

Posts: 9
Registered: 8/29/09

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

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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 LMI-toolbox'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.