In existing work of sliding mode observers for descriptor systems, a necessary condition is that the system must be infinitely observable. This paper presents a scheme that circumvents that condition, by reformulating the system as a reduced-order system where certain structures in the system matrix are manipulated and certain states are treated as unknown inputs. Following that, a sliding mode observer (SMO) is implemented on the reduced-order system where state and fault estimation can be achieved. Necessary and sufficient conditions of this scheme are also presented. Finally, a simulation example shows the effectiveness of the proposed scheme.

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This paper presents a novel scheme for estimating states and faults for a class of infinitely unobservable descriptor systems using sliding mode observers (SMOs). Treating certain states of the original infinitely unobservable system as unknown inputs results in a reduced‐order system that is infinitely observable. Then by designing the SMO based on the reduced‐order system, state estimation and fault reconstruction is achieved, thus relaxing the infinite observability requirement of the original system. The necessary and sufficient conditions in terms of the original system matrices are also investigated. A simulation example verifies the claims made in this paper.

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