Here are some things which jumped out at me from a casual glance at your program.
Is
T(2,2)-eye(2)==semidefinite(2);
X1(2,2)-eye(2)==semidefinite(2);
X2(2,2)-eye(2)==semidefinite(2);
X3(2,2)-eye(2)==semidefinite(2);
X4(2,2)-eye(2)==semidefinite(2);
what you really want? T(2,2), X1(2,2), etc. are individual scalars, not the entire matrices. These constraints are equivalent to T(2,2) >= 1, X1(2,2) >= 1, etc. I doubt that’s what you want. Perhaps you want
T-eye(2)==semidefinite(2);
X1-eye(2)==semidefinite(2);
X2eye(2)==semidefinite(2);
X3-eye(2)==semidefinite(2);
X4-eye(2)==semidefinite(2);
Declaring a variable as semidefinite diagonal is just the same as declaring it diagonal nonnegative, although i don’t know whether CVX and/or the solver are smart enough to recognize that and simplify the model accordingly.
You can try omitting certain constraints until you get feasibility. Also, you can use nonnegative slacks, which in the case of semidefinite constraints would involve changing LHS to LHS + s*eye(n) (for appropriate value of n)., Then minimize sum of slacks instead of the original objective, to help you diagnose the infeasibility.
I have no idea what your model is supposed to represent, so i can’t tell you what is correct or not. But based on my observations above, perhaps there’s more wrong with your code than the suspicious things i pointed out.