A convex feasibility problem or A convex optimization problem

I have a question and ask you for help.
suppose A(s1,s2)=A0+s1*A1+s2*A2,
where A0, A1 and A2 are 44 constant, known matrix.
I want to find out a constant 4
4 matirx P>0 which subjects to
P*A(s1,s2)+A(s1,s2)'P < 0
point (s1,s2) is in the rectangular region [a,1]*[b,1] ,
where 0<a<1,0<b<1.
How can I solve this problem?
Thank you very much,sincerely.

This problem violates the DCP ruleset as written, and I don’t see a way to represent it in a compliant manner. But this is a Lyapunov stability problem, and if it can be written in a convex form, likely as a semidefinite program, then the control community is going to know how to do it. I suggest scouring the control literature for information on this; perhaps Linear Matrix Inequalities in System and Control Theory (downloadable copy at the link).

Dear mcg:Thank you very much for your answer. Maybe I’ll look for details with relative literature.