That produces {real affine}/{real affine}, which is not allowed in CVX, and is non-convex.

It is a linear fractional form which potentially, depending on the rest of the program, could be reformulated as a convex problem for CVX. But that would require that the denominator always be positive, or alternatively, always be negative.

Yeah, you are right, the formulation seems like a linear fractional form and the denominator always be positive, but I have no idea about how to convert it into a convex function which CVX could accept it, by the way, the rest of my problem are all convex formulation, practically, belongs to SDP problem.

You can read the material on linear fractional forms in https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf . As for whether that will work with the rest of your problem, including SDP constraints, I donâ€™t know.