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Active fault detection consists of finding an auxiliary input signal such that its use allows detection of faults using a multi-model framework. Faults can be detected during a test period that would otherwise not be possible to detect during normal operation using passive tests. In this paper, we consider the problem of optimal exogenous signal design for a linear uncertain system controlled by a linear feedback. This signal design is based on controller design criteria of linear quadratic regulators (LQR). Optimal exogenous signal design for short test periods is considered first. An efficient method is developed to solve the corresponding finite time-horizon optimization problem. Then the asymptotic behavior of the robust fault detection problem and its stationary optimal solution is considered. The optimal exogenous signal for the stationary case is given based on a frequency analysis of the solution. This signal can be used as an approximation on longer interval finite time-horizons. It is shown that a suitable feedback can reduce the cost function compared with the open-loop case.