Solving differential linear matrix inequalities using LMI

Hi,

I have the next problem and I tried to read about LMI to figure out how to solve it but I couldnt understand.

I have the values of A(t),B(t),Gamm(t) and R for any t. I understood how to use "lmivar" and "lmiterm" however I dont know how eventually to get the result for X and L which im looking for.

I thought about "feasp" but I got stuck because of the derivative of X.

Thank you very much.

[YICHENG XU]

I believe LMILAB is not built to solve differentiable LMI. They are given to solve problems like "PA+A^TP<0" or so. Solving differentiable LMI requires to search on all t, which results to infinitely many LMIs. There is some workaround, I sugguest you to take a look at the book written by José C.Geromel "Differential Linear Matrix Inequalities". In Chanpter 9, there are numerical examples, which might help.