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Topic: How to change this inequality to LMI form?
Replies: 1   Last Post: Aug 29, 2009 12:48 PM

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J

Posts: 9
Registered: 8/29/09
Re: How to change this inequality to LMI form?
Posted: Aug 29, 2009 12:48 PM
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"Qiming Zhao" <widemanzhao@yahoo.com.cn> wrote in message <h15jth$8l9$1@fred.mathworks.com>...
> Here is an inequality:
> A'P + PA - P*B*inv(R)*B'*P + e*P*D*D'*P + (1/e)*E'*E < 0.
> I use Schur complement lemma to change it into LMI:
> [ A'P+PA+(1/e)*E'*E PB PD
> * -R 0
> * * -inv(e)] < 0
> Using LMI toolbox, the message "These LMI constraints were found infeasible" pops up.
> The correct answer is that the LMI is feasible. Is the LMI form I translate wrong?
> What is the right form of the LMI?
> Thanks in advance!


It looks like your LMI should be

[A'P+PA+1/e E'*E PB PD
* inv(R) 0
* * -inv(e) ] < 0

I am having trouble with feasp returning "cannot determine feasibility" and also with mincx returning solutions that it thinks are feasible, but in fact are not. Have you found these sort of issues in your work?

-J



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