A Lifting Based Approach to Observer Based Fault Detection of Linear Periodic Systems

In this note, an approach based on lifting is introduced for the observer based fault detection (FD) of linear discrete-time periodic systems. The main contribution of this note is to give an analytic expression to transform the linear time-invariant (LTI) observer based residual generator designed based on the lifted LTI reformulation of the periodic system into a periodic observer based residual generator to reduce detection delay. The result enables a systematic transfer of the existing observer based FD methods for discrete LTI systems to discrete-time periodic systems.