A common requirement implicit in the Current methods for the design of robust state estimators and robust fault detection filters is that the first Markov matrix must be non-zero, and indeed, full rank. We relax both of these restrictions in this paper to allow the applicability to a wider range of systems. The extended results are then applied to an aircraft fault detection for which the restrictive condition is not satisfied. (C) 2008 Elsevier Ltd. All rights reserved.