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A new direct approach to jump detection in linear time-invariant stochastic systems is considered in this paper, leading to a class of simple detection algorithms based on the explicit computation of the generalized likelihood ratio. While most of the already known methods perform the detection by observing the residuals of the Kalman-Bucy filter, here the output of the system is directly used for the detection, obtaining a larger class of algorithms which seems particularly convenient when state estimation is not required. Though the present approach is suitable only for time-invariant systems, its great flexibility allows the algorithm to be tightened to a particular application by changing such fundamental parameters as time-delay and observation interval. The practical application of the method to power systems perturbation detection is developed in the second part of the paper, where simulation results are presented as well. The discussion of the application shows as a precise qualification of the performance in terms of false alarm rate and probability of detection yields simple design criteria for the algorithm.