Observer-based fault diagnosis for structured systems

We consider the fault detection and isolation (FDI) problem for linear systems with disturbances. We try to design a set of residuals through a bank of observers, in such a way that the transfer from the disturbances to the residuals is zero and the transfer from the faults to the residuals is diagonal. We deal with this problem when the system under consideration is structured, that is, the entries of the matrices which define the system are either fixed zeros or free parameters. To structured systems one can associate in a natural way a directed graph. We are then able to give a necessary and sufficient condition under which the FDI problem has a solution for almost any value of the free parameters. This condition is simply expressed in terms of particular paths in the associated graph