Optimal control problem for rectangular descriptor systems via dynamic output feedback

This paper deals with the optimal control problem by dynamic output feedback for rectangular descriptor system with disturbance. The design of dynamic output feedback contains two parts. The first one is given to make the rectangular descriptor system to be squared and the poles of the closed-loop system can be placed at arbitrarily approximation to the given positions. The other one is composed of Proportional-Integral (PI) observer and state feedback controller. The full-order PI observer which can estimate the state variables and disturbances is constructed to obtain the state information. Using the state information from the observer, the optimal disturbance rejection control law is proposed and the given quadratic performance index can be described in a simple form related to the solution and the initial value of the closed-loop system. Then a corresponding algorithm to minimize the quadratic performance index is proposed in which an optimal controller can be obtained. Finally, a numerical example is given to show the effectiveness and correctness of the proposed method.