I can not write X = eye(2); X(1,1)=sdpvar(1,1)!

This is because of the way the object orientation works in MATLAB (a user-class object cannot be assigned into a built-in class object). The prefered pattern to code in YALMIP is to use concatenation, i.e. create it as X=[sdpvar(1,1) 0;0 1].

A possible alternative is the command X=double2sdpvar(eye(2));X(1,1) = sdpvar(1,1); (not recommended though as it misses the core philosophy of YALMIP of being completely natural to beginners)