Robust fault reconstruction for a class of nonlinear systems

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This paper proposes two novel observer schemes for reconstructing faults in systems where the fault enters the state and output equations via nonlinear functions, which has not been considered in the literature. Two design methods are presented: one for the case where the fault dynamics are known and can be expressed as a polynomial function of time, and another for the case where the fault dynamics are unknown. The gains of the observer are designed using linear matrix inequalities (LMIs) such that the root-mean-square (RMS) gain from the uncertainties (or disturbances) to the fault reconstruction error is bounded. Necessary conditions for the feasibility of the LMIs are presented. Finally, a simulation example is shown to demonstrate the efficacy of the proposed scheme.