This contribution aims the problem about controller synthesis in H2 and H∞ for linear time invariant systems (LTI), by means of the extended static feedback of the output. The method consists of designing feedback gains for the injection of the output and its derivatives, which corresponds to the control signal. Conditions for the existence of such controllers are established. The stabilization problem is formulated in the context of linear matrix inequalities (LMI). Multiobjective Performance Indices are also considered.