Observer-based fault detection and isolation for structured systems

Abstract

Fault detection and isolation (FDI) problems are here consid- ered for linear systems with faults and disturbances. We design a set of ob- server-based residuals in such a way that the transfer from the disturbances to the residuals is zero, and the transfer from the faults to the residuals al- lows fault isolation. We are interested in obtaining a transfer function from faults to residuals with either a diagonal structure (i.e., a dedicated struc- tured residuals set) or a triangular one. 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. To a structured system, one can associate in a natural way a directed graph. We can then provide necessary and sufficient conditions under which the FDI problems have a solution for almost any value of the free parameters. These conditions are simply expressed in terms of input-output paths in the associated graph. Index Terms—Fault detection and isolation, graph theory, model-based approach, structured residuals, structured systems.