This paper proposes a fast fault estimation (FE) method for a class of linear time-invariant systems, which relaxes the strict observer matching condition. Firstly, the integration unknown input observer is designed for the more widely left invertible systems. Secondly, for strongly observable systems, by digesting the idea of a finite-time observer, the finite-time integration unknown input observer is designed, and the faults are estimated exactly in pre-designed arbitrary finite time. Furthermore, for strongly detectable systems, after the system decomposed into strongly observable part and nonstrongly observable part, faults are able to be reconstructed very rapidly due to the finite-time observation of the strongly observable subsystem. The simulation results illustrate the effectiveness and the advantage of the proposed fast fault estimation schemes.
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