Optimal disturbance rejection for descriptor systems based on dynamic output feedback

The linear-quadratic optimal disturbance rejection problem by dynamic output feedback for descriptor system is considered in this paper. This dynamic output feedback controller contains two parts: PI observer and state feedback controller. The observer is used to estimate the state variables, and the state feedback controller is to realize the optimization. Firstly, a sufficient condition for the existence of full- and reduced-order PI observers is given. Secondly, in light of the state information from the observer and the optimal feedback control theory, the optimal disturbance rejection control law is proposed such that the closed-loop system is admissible and the given performance index achieves the optimization. Finally, two numerical examples are used to demonstrate the effectiveness and correctness of the proposed approach.