Yes, your CVX program implements the model provided in your comment lines and appears to be correct.
However, with the CVX program as you have entered, you don’t need SDP mode, i.e,. you don’t need the
cvx_begin sdp. Alternatively, if you do use
cvx_begin sdp, you could change your semidefiniite constraints to
-X+(5-0.3 * y) * eye(2) >= 0;
X+y * eye(2) >= 0;
But again, let me make clear that your program as provided appears to be correct.
Note that in SDP mode, your constraint
1.5 * X(2,2)+X(1,2)>=2 is interpreted, as desired, as an element-wise constraint, because it is one-dimensional. You might want to re-read http://cvxr.com/cvx/doc/sdp.html to make sure you understand everything.