Observer-based fault detection and isolation for 2D state-space models

In this paper, the fault detection and isolation problems for two-dimensional (2D) state-space models are investigated, both when no disturbances affect the system and when they actually do. Basing on some old results about dead-beat observers [Bisiacco, M. (1986) IEEE Transactions on Automatic Control, AC-31, 676-680] and on some recent results about dead-beat unknown input observers (UIOs) (for 2D systems affected by disturbances) [Bisiacco, M. & Valcher, M. E. (2004) International Journal of Control 77(9), 861-876], we develop a complete theory of dead-beat (possibly unknown input) observer-based fault detectors and isolators (FDIs). Necessary and sufficient conditions for the existence of a dead-beat observer-based FDI or for the existence of a dead-beat UIO-based FDI are derived, and constructive procedures for obtaining such FDIs are described in detail.