On fault detectability and isolability

We review several existing detectability and isolability definitions. We argue that two types of definitions have to be distinguished. On one hand, intrinsic definitions capture the signature of the fault on the system. On the other hand, performance-based definitions involve indexes of performance of fault detection algorithms. In particular, since many fault detection algorithms involve a residual generation mechanism, such definitions may capture, among other performance indexes, the signature of the fault on the residuals. In the particular case of sensor and actuator faults in linear dynamic systems, we exhibit an equivalence among several definitions.