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This article proposes a method on simultaneous estimation of the system fault and sensor fault for a kind of the Markovian jump system with generally uncertain transition rates. In order to estimate these system fault and sensor fault, we first design a novel reduced-order observer, in which the gain matrix can not only decouple the existed unknown input, but also compel the observer error dynamic system to be stable. Then, the existing conditions of the proposed observer are derived in terms of linear matrix inequalities, making the problem tractable. Finally, an example is provided to illustrate the effectiveness and validation of the proposed method. [ABSTRACT FROM AUTHOR]