New results in robust fault reconstruction for a class of non-infinitely observable descriptor systems

This paper presents a sliding mode observer (SMO) scheme for robust fault reconstruction in descriptor systems that are not infinitely observable. The proposed scheme improves on existing schemes that do not consider the effect of disturbances which can corrupt the reconstruction, or require restrictive conditions. Some states are re-expressed in terms of other states, and certain other states are treated as unknown inputs, thereby forming a reduced-order system. A SMO is then implemented onto this reduced-order system to reconstruct the fault. Linear matrix inequalities (LMIs) are used to design the observer such that the \mathscrL2 gain from the disturbances to the fault reconstruction is minimised. The existence conditions for the scheme are investigated. Finally, a simulation example is presented to demonstrate the efficacy of the proposed scheme.