LMI simplification

[mohmmed ahmed]

Dear Johan

can you tell me is  this simplification  of LMsI in the attachment is correct...

I mean what I done in the attachment is it correct or there is mistake

Thanks

[Johan Löfberg]

Incorrect, well at least very confusing

Your first application of a Schur complement is correct, but the end result is a nonlinear SDP, so what would you have it for?. The second batch is sort of correct, but it adds no information as the last constraint follows from the (2,2) block in the second to last LMI, and the second-to last LMI already is encoded in the nonlinear (2,2) block that you have in the first nonlinear SDP you derived.

Perform a Schur complement involving both X and Y from start. However, you will get a nonlinear product of X and P ( and Y and P) which you do not want I guess.

Read this book
http://stanford.edu/~boyd/lmibook/

In particular Chapter 7 on standard tricks

[mohmmed ahmed]

you mean  the final answer

A'P+PA>0

is not correct

??

[Johan Löfberg]

x>0 is completely redundant if you have [x y;y z]>0