Design of finite‐time convergent functional observer for descriptor systems: Application to fault estimation

In this paper, a finite‐time functional observer design for linear time‐invariant descriptor systems is presented. A generalized observer based on additional degrees of freedom is developed. This observer can be considered of a general structure since the existing proportional observer (PO) and proportional‐integral observer (PIO) constitute its particular cases. The main contribution is to generate a finite‐time convergent functional observer for descriptor systems by combining two generalized functional observers. The obtained results are applied to the simultaneous state, sensor, and actuator faults estimation. A numerical example is given to illustrate the approach. The obtained results show that the observer is robust in presence of uncertainties, compared to its particular cases.