This study investigates general model-based incident handler's asymptotic behaviors against cyber attacks to control systems. The attacker's and the defender's dynamic decision making is modeled as an equilibrium of a dynamic signaling game. It is shown that the defender's belief on existence of an attacker converges over time for any attacker's strategy provided that the stochastic dynamics of the control system is known to the defender. This fact implies that the rational behavior of the attacker converges to a harmless action as long as the defender possesses an effective counteraction. The obtained result supports the powerful protection capability achieved by model-based defense mechanisms.