Design of Unknown Input Observer for Fractional Order Singular Systems with Application in Fault Diagnosis

This paper investigates the design of an unknown input observer (UIO) for fault diagnosis in linear fractional order singular systems. A parametric approach is proposed for the design of this unknown input observer and the necessary and sufficient conditions for the existence of the proposed observer are derived. Then based on the stability analysis of fractional order systems, a systematic design approach is presented to ensure the convergence of the estimation errors. The proposed observer is nonsingular, and uses only the original coefficient matrices to reconstruct the actuator faults. Also, both the unknown inputs appearing in the system and output equation can be decoupled using only the available inputs and measurable output signals. The convergence conditions of this observer are derived in terms of linear matrix inequalities (LMI).