The problem of robust fault detection in command inputs in the presence of modelling errors in linear time-invariant systems is addressed. It leads to a hypothesis test with a test statistic taking form of a weighted quadratic sum of independent normally distributed variables. It is rather difficult to compute the threshold for such a test and the corresponding error probabilities in an exact manner. Instead, the approximative results are derived by assuming assymptotic distribution of the test statistic towards normal distribution. Convergence conditions in case of growing number of summands are presented. Performance of the resulting detector is demonstrated on a simulated DC motor-generator rig.