Optimal sensor location for fault detection and isolation in linear structured systems

We consider here the Fault Detection and Isolation (FDI) problem for linear systems. We design a set of observer-based residuals, in such a way that 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 system matrices are either fixed zeros or free parameters. This problem was solved recently in terms of the graph that one can associate in a natural way to a structured system. We are concerned in this paper with the case where the FDI solvability conditions are not satisfied. We consider that some internal states can be measured at some cost and wonder if the problem is solvable with these new measurements. If this is possible we try to reach the solvability conditions at minimal cost. These problems are solved using the bipartite graph of the system.