what is effect on the solution of LMI if we have many variables unknow

[mohmmed ahmed]

hi

In general

 can you tell me what is effect on the solution of LMI if we have many variables unknow required to find solution?? for example

assume you have

A'P+PA<0

A'P+PA+Q<0

in the first LMI we have  one unknow variable P

in the second LMI we have two unknow varible P and Q

is there effect on solutoion if we increase number of variable ??

[Johan Löfberg]

What do you mean with effect on solution?

'Both forms you've written as badly posed though (strict inequalities cannot be used in practice, and since they are homogenous, solutions arbitrarily close to zero will be feasible, if the feasible space is non-empty)

[mohmmed ahmed]

Dear jouan

i talk general assume you have tow LMI  ...first one hase one variable to be find

second one has 5 variables to be find.

Does the solution of fist LMI will be more accurate  than second??

what is the effect now in the solution if we have many variable to be find

[Johan Löfberg]

Accuracy does not depend on the number of variables in the model (in theory, in practice more/other variables might lead to different numerical properties etc). It will simply have to spend more time to find a solution with the desired accuracy

[mohmmed ahmed]

can you tell me...in general

 who will effect in the accuracy of solution?

who well reduce facing infiseable solution ? 

[Johan Löfberg]

I don't understand what you are asking. I advice you to read some papers on the solution of semidefinite programs (such as the papers describing SDPT3 or SeDuMi, or some general review paper)