Robust fault reconstruction for a class of non-infinitely observable descriptor systems using two sliding mode observers in cascade

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Existing sliding mode observer (SMO) schemes for fault reconstruction in descriptor systems require stringent conditions, or do not consider disturbances which can corrupt the reconstruction. In this paper, we present a two-observer scheme that overcomes these limitations by treating certain states as unknown inputs, thereby formulating a reduced-order infinitely observable system. A SMO is implemented onto this system to reconstruct certain faults, and its switching feedback term is fed into another SMO to reconstruct the remaining faults. Linear matrix inequalities (LMIs) are used to design observer gains in order to minimise the L2 gain of the disturbances on the fault reconstruction. The existence conditions of the scheme are investigated and are found to be less restrictive than those from other schemes in the literature, and thus the scheme is applicable to a wider class of systems compared to existing schemes. Finally, a simulation example demonstrates the efficacy of the proposed scheme.