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Thread Subject:
Gevp problem issue in an iterative LMI problem

Subject: Gevp problem issue in an iterative LMI problem

From: Rafael Herrera

Date: 17 Apr, 2013 18:14:09

Message: 1 of 2

Hi guys.

This is my first time here and I really hope you can help me.

I´m working with an control design method that uses an Iterative Linear Matrix Inequality (ILMI) and I´m having some issues trying to implement one of the steps (the gevp one). The method is presented on the paper "Static Output Feedback Stabilization: An ILMI Approach".

The regular matlab gevp problem (http://www.mathworks.com/help/robust/ref/gevp.html) states the LMI by C(x) < D(x), 0 < B(x) and A(x) < ?B(x), and the problem is to minimize ?. Well, my problem states the LMI as follows:

[(Pi + PiA - XiBB´Pi - PiBB´Xi + XiBB´Xi- ?Pi) (B´Pi+FC)´
 (BTPi+FC) -I ] < 0

It means that my ? that shall be minimized isn´t in the regular matlab form and I can´t imagine how to put this matrix of LMI into the 3 LMIs form above.

I would appreciate a lot your help because I´m really lost.

Thank you

Subject: Gevp problem issue in an iterative LMI problem

From: Johan Lofberg

Date: 18 Apr, 2013 06:13:10

Message: 2 of 2

"Rafael Herrera" <rafael.herrera01@gmail.com> wrote in message <kkmoph$fo4$1@newscl01ah.mathworks.com>...
> Hi guys.
>
> This is my first time here and I really hope you can help me.
>
> I´m working with an control design method that uses an Iterative Linear Matrix Inequality (ILMI) and I´m having some issues trying to implement one of the steps (the gevp one). The method is presented on the paper "Static Output Feedback Stabilization: An ILMI Approach".
>
> The regular matlab gevp problem (http://www.mathworks.com/help/robust/ref/gevp.html) states the LMI by C(x) < D(x), 0 < B(x) and A(x) < ?B(x), and the problem is to minimize ?. Well, my problem states the LMI as follows:
>
> [(Pi + PiA - XiBB´Pi - PiBB´Xi + XiBB´Xi- ?Pi) (B´Pi+FC)´
> (BTPi+FC) -I ] < 0
>
> It means that my ? that shall be minimized isn´t in the regular matlab form and I can´t imagine how to put this matrix of LMI into the 3 LMIs form above.
>
> I would appreciate a lot your help because I´m really lost.
>
> Thank you

You cannot put it in standard GEVP form, that is exactly what the paper is about. They propose an iterative approach where they solve a sequence of standard LMIs and GEVPs keeping some of the variables fixed and optimizing over the other variables.

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