Descriptor Observers for Robust Fault Reconstruction in a Class of Nonlinear Descriptor Systems

This paper presents a robust fault reconstruction scheme for a class of nonlinear descriptor systems that is affected by disturbances. The fault enters the system both linearly and through nonlinear functions in both the state and output equations. The system is first re-expressed into a form which is easier to manipulate. Two cases are considered: in the first case, the fault is present in the nonlinear function of the output equation, whereas in the second case, the nonlinear function of the output equation does not contain the fault. In each case, a nonlinear descriptor observer is used to reconstruct the fault, where the gains of the observer are designed using linear matrix inequalities such that the effect of disturbances on the fault reconstruction is bounded. As a result of their structure, the proposed descriptor observers do not require restrictions on the rates of the input and disturbances (unlike in observers using a state-space structure) which makes the proposed observers more widely applicable. Finally, two simulation examples are performed to verify the performance of the proposed observers.