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This study considers the application of a continuous non-linear fault estimation system to reconstruct the state vector and actuator faults for multivariable linear systems, in which the effects of faults are modelled as additive unknown inputs. To estimate the state, a continuous function is introduced to compensate the effects of fault and disturbance. It is shown that if the state reconstruction error converges to zero asymptotically, then the continuous function can be used as a reconstruction of fault and disturbance. The feasibility of the design scheme can be checked by solving a linear matrix inequality. Also, the design scheme does not rely on any particular canonical form of the model, so coordinate transformation is not necessary. Using the similar approach, a disturbance decoupled fault reconstruction scheme is also proposed. Finally, a design example is given and the reconstruction of both multiplicative fault and additive disturbance are simulated.