Equality Constraints in LMI

I am solving a LMI to find matrix P but I want to ensure that P*B=C' where B and C are state space matrices of a system. That means I want to incorporate equality constraint in LMI. How to do it? Code is given below

clear all;

clc;

A= [ -2 -1 -1; 1 0.2 -2.3; 1 1 -5.7];

B= [ 1 0; 0 1; 1 1];

C= [ 2 0 0; 0 0 2];

setlmis([])

P = lmivar(1,[3 1]);

phi = lmivar(2,[3 2]);

l = lmivar(1,[1 1]);

lmi1 = newlmi

lmiterm([lmi1 1 1 P],1,A,'s')

lmiterm([lmi1 1 1 phi],1,C,'s')

lmiterm([lmi1 1 1 l],1,1)

lmiterm([lmi1 1 2 P],1,1)

lmiterm([lmi1 2 2 0],-1)

lmi2 = newlmi

lmiterm([-lmi2 1 1 P],1,1) %P>0

% get the LMI system

G= getlmis;

% Solve

[tmin, xfeas] = feasp(G);

% Extract variable

P1 = dec2mat(G,xfeas,P)

phi1 = dec2mat(G,xfeas,phi)

l1 = dec2mat(G,xfeas,l)

L = inv(P1)*phi1

[AdamsK]

Did you ever find a solution to this problem? If so, do you remember what it was now that nearly 10 years have past? I have a similar situa5ion and am looking for a solution.