Help with LMI system with two LMIs

Hi everyone, I need to solve the following LMI system:

P1C1 + C1TP1 + [aP1 + bP2] < 0 LMI1 P2C2 + C2TP2 + [cP1 + dP2] < 0 LMI2

Where a,b,c,d are constants. I need to find P1 and P2 that satisfies those LMIs.

Can I solve such a system with the LMI toolbox? Can I model this in one LMI?

Where I got so far:

if true
  % setlmis([]) 
%  p1 = lmivar(2,[8,8])
%  p2 = lmivar(2,[8,8])
% 
% lmiterm([1 1 1 p1],1,C1)     % LMI #1 
% lmiterm([1 1 1 p1],C1',1)     % LMI #1 
% lmiterm([1 1 1 p1],a,1)     % LMI #1 
% lmiterm([1 1 1 p2],b,1)     % LMI #1 
% 
% lmiterm([1 2 1 p2],1,C1)     % LMI #2 
% lmiterm([1 2 1 p2],C1',1)     % LMI #2 
% lmiterm([1 2 1 p1],c,1)     % LMI #2 
% lmiterm([1 2 1 p2],d,1)     % LMI #2 
% 
% lmisPP = getlmis
% [tmin,xfeas] = feasp(lmisPP);
% PP1 = dec2mat(lmisPP,xfeas,p1);
% PP2 = dec2mat(lmisPP,xfeas,p2);

end

Well, with this I get two answers for P1 and P2 (PP1 and PP2), but seems like the answer is not always correct. Can someone help me improve this code? This is the first time I work with LMI, so I'm not sue about the model.

Thank you so much!!