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This paper presents a replay attack detection method that addresses the performance loss of watermarking-based approaches. The proposed method injects a sinusoidal signal that affects a subset, chosen at random, of the system outputs. The presence of the signal in each one of the outputs is estimated by means of independent observers and its effect is compensated in the control loop. When a system output is affected by a replay attack, the loss of feedback of the associated observer destabilizes the signal estimation, leading to an exponential increase of the estimation error up to a threshold, above which the estimated signal compensation in the control loop is disabled. This event triggers the detection of a replay attack over the output corresponding to the disrupted observer. The effectiveness of the method is demonstrated using results obtained with a quadruple-tank system simulator.