Approach to fault detection of time‐delay systems using functional observers

A new methodology is reported for designing functional observers to detect actuator faults of a class of time‐delay systems where the matrix pair ( A , C ) is not observable. First, a generalised state transformation is used to transform the system into new coordinates where the delay term associated with the state vector is injected into the system's output and input. Then, a minimum‐order functional observer is designed to construct a residual function that can trigger system faults. The finding is significant as it is now possible to detect faults of time‐delay systems where the pair ( A , C ) is not required to be observable. A numerical example is given to illustrate the effectiveness of the proposed design approach.