After using S-procedure, there existing quadratic term in the matrix

The figure below shows a constraint, the optimize variable is qu, is this constraint convex? if yes, can the CVX deal with it? Iam looking forward to your reply. Thank you.

That is a BMI (Bilinear Matrix Inequality, which is a type of nonlinearSDP), so non-convex. So, it is out of the capability of CVX, unless you have a reformulation into a linear SDP. You could consider using YALMIP.

Ok, thank you very much.