How to Define the Absolute function in the Constraint of SDP

All the constraints containing ab are non-convex, because abs is the only nonlinear (in the optimization variables) thing on either side of the <= So no reformulation to convex would be possible, unless it turned out that all the constraints were redundant and could be eliminated, which I presume is not the case.

Unfortunately, your topic has earned the dreaded nonconvex categorization for the first time in a while.