Fault detection for systems with multirate sampling

We consider multirate sampled-data systems with a single input sampling period and multiple output sampling periods that are integer multiples of the input sampling period. We modify the Chow-Willsky approach to obtain a residual generator design for this class of multirate systems. We derive conditions for the existence of residual generators that guarantees fault detection and disturbance rejection. We also derive conditions of the existence of a structured residual generator. An example is presented to illustrate our approach.