Finite Unobservability Subspaces for Time-Delay Systems with Application to Fault Detection and Isolation

This paper introduces the notion of finite unobservability subspace for time-delay systems and an algorithm for obtaining these subspaces is presented. Then Fault Detection and Isolation (FDI) filters for retarded time-delay systems with unknown time-varying delays are designed based on our developed geometric framework. A bank of residual generators is then designed so that each residual is affected by one fault and is partially decoupled from the others while the H∞ norm of the transfer function between the disturbances and the uncertainties in delays and the residual signals are guaranteed to remain less than a prescribed value. Simulation results presented demonstrate the effectiveness of our proposed FDI algorithms.