I tried in the YALMIP. By using the mosek solver, the solver does not support that constraint, i.e. inv_pos(a)<=trace(W).
I have not tried in the cvx. (I also think it can support the above constraint.)
Because under using solver (mosek) and solving the same SDP problem, the cvx can not achieve the right solution. The scaling of my problem is bad. There exist some small values. e.g. 0.0122e-4, 0.1245e-4 and so on.