This paper presents a novel anomaly detection designed to detect integrity attacks in discrete-time linear cyber-physical control systems. Our approach involves applying a bounded time-varying arbitrary sequence to scale the control gain. We assume that this sequence remains concealed from attackers but is known to the anomaly detection unit. We provide rigorous mathematical guarantees that crafting stealthy attacks is impossible in discrete-time linear cyber-physical control systems safeguarded by our proposed approach, even in complex scenarios where attackers are aware of system dynamics and capable of eavesdropping and manipulating both input signals and sensor measurements. Additionally, we establish stability guarantees for the system during attack-free operation. Our findings underscore the reliability of the proposed method in safeguarding discrete-time linear cyber-physical control systems against malicious activities.