Design of unknown input proportional-multiple fractional order integral observer for fractional order singular systems with application in fault diagnosis

This paper investigates the design of an unknown input proportional-multiple fractional order integral observer (UIPMIαO) for fault diagnosis in fractional order singular systems. It is assumed that the gα-th derivative of the fault vector is bounded and a parametric approach is proposed for the design of the unknown input observer with s fractional order integral actions. First, 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. Both the unknown inputs appearing in the system and output equation can be decoupled using only the available inputs and measurable output signals. The effectiveness of the proposed method is illustrated with a numerical example.