Condition of Existence for Reduced-Order Observer and Its Application in Fault Detection and Diagnosis

The condition of existence of a reduced order observer for linear systems with generalized unknown inputs is studied. The existence condition is then transformed to the stabilizability of the assistant system through a generalized inverse matrix and the assistant system. The reduced order observer is applied to fault detection and diagnosis by transforming the linear system with unknown inputs to the standard form of linear system with generalized unknown inputs. By the simulation of an electrical servo system, it is shown that the method can detect and diagnose faults rapidly when several faults occur simultaneously.