This paper deals with the design of an estimator-based supervisory Fault Tolerant Control (FTC) scheme for Linear Time Invariant (LTI) systems. A formal stability proof based on dwell-time conditions is established in case where the state of the detection filter does not correspond to the plant state, as in classical (Luenberger) observer-based approaches. In this context, fault isolability could be improved leading to an enhanced distinguishability between all possible operating modes. The efficiency of the proposed technique is illustrated on a numerical example.