H control theory provides a systematic frequency shaping method of control systems. The existence condition of the solution for so called standard H control problem and the form of the H controller are derived in 1989. One of the most important feature of the controller is that it has many free parameters which can be chosen independently of the H control. On the other hand there is a criticism that the time response of prototypal H control systems is slow. Therefore in this paper we introduce an H2 control optimization by taking advantage of the free parameters to expect the improvement of the time response of the H control system. In this paper we consider state feedback case. The free parameters of state feedback H controller are not directly obtained from well known results since this problem is a kind of non-standard problem. Therefore, in the first place, we will get them via reviewing the FI (ful information) case. Then the free parameters of the state feedback H controller are shown based on the corrected FI solution. These parameters are next used to optimize an H2 control objective in the H control system.