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We propose a framework for inversion-based estimation of certain categoriesof faults in discrete-time linear systems. The fault signal, as an unknowninput, is reconstructed from its projections onto two subspaces. One projectionis achieved through an algebraic operation, whereas the other is given by adynamic filter whose poles coincide with the transmission zeros of the system.A feedback is then introduced to stabilize the above filter as well as toprovide an unbiased estimate of the unknown input. Our solution has twodistinctive and practical advantages. First, it represents a unified approachto the problem of inversion of both minimum and non-minimum phase systems aswell as systems having transmission zeros on the unit circle. Second, thefeedback structure makes the proposed scheme robust to noise. We have shownthat the proposed inversion filter is unbiased for certain categories offaults. Finally, we have illustrated the performance of our proposedmethodologies through numerous simulation studies.

Unbiased Inversion-Based Fault Estimation of Systems with Non-Minimum Phase Fault-to-Output Dynamics