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A multiconstrained reduced-order fault estimation observer (RFEO) design is proposed to handle the case of abrupt and time-varying faults, and a comparison with full-order fault estimation observer is discussed in detail. Then, by introducing a slack matrix, a new multiconstrained RFEO result is obtained to reduce conservatism generated by the conventional method. Further, the present authors investigate robust RFEO design to cope with external disturbances. 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