This paper investigates the security issue of the data replay attacks on the control systems. The attacker is assumed to interfere with the control system process in a steady-state case. The problem is presented as the standard way to attack, which is storing measurements and replay ing them in further times to the system. The controller is assumed to be the LQG controller. The main novelty in this paper can be stated as proposing a different attack detection criterion by using the K-L divergence method to cover more general control system problems with these attacks and with higher-order dynamics. Also, there exists a packet-dropout feature in transmitting the data as another contribution of the paper. Formulations and numerical simulations prove the effectiveness of the newly proposed attack detection procedure by having a quick response to occurred attacks. Although, in previous approaches, the trade-off between attack detection delay or LQG performance was significant, in this approach it is proved that the difference in this trade-off is not considered in early moments when the attack happens since the attack detection rate is rapid and thus, these attacks can be stopped with defense strategies in the first moments with the proposed attack detection criterion.