Sensor fault diagnosis in fractional-order singular systems using unknown input observer

This paper investigates the design of an unknown input observer for sensor fault diagnosis in linear fractional-order singular systems. The considered system is rectangular in general form. The necessary and sufficient conditions for the existence of the proposed observer are derived, and a systematic design approach is presented. The designed observer is nonsingular and uses only the original coefficient matrices to reconstruct the sensor faults. The proposed diagnosis method can decouple both the unknown inputs appearing in the system dynamics and the output equation, using only the available inputs and measurable output signals. The asymptotic stability conditions of the designed observer are obtained in terms of linear matrix inequalities. Moreover, the proposed approach is developed for sensor fault diagnosis in fractional-order singular one-sided Lipschitz systems. The convergence conditions of the designed nonlinear observer are derived in terms of linear matrix inequalities by introducing a continuous frequency distributed equivalent model and using indirect Lyapunov approach. Finally, the proposed approach is applied to a machine infinite bus system and a numerical example to demonstrate its effectiveness.