Welcome to the forum!!
The formula using norm should work, but it should have sqrt(H) in place of H in the argument of norm.
By inverse of ru, I presume you meanreciprocal. That is not allowed in CVX, because norm is convex, not concave (as would be needed for inv_pos or pow_p) .So that raises the possibility that your optimization problem is not convex. I don’t know whether it is, because I haven’t seen what you intend to to with the reciprocal of norm, If the desired use is of the form {affine expression}/norm(...) >= constant, it could be reformulated as {affine expression} >= constant*norm(...), which is a convex constraint and would be accepted by CVX.
So your first step is to prove your optimization problem is convex.