一般广义离散系统动态输出反馈H∞控制器设计

Design of dynamic output feedback H_∞ controller for common singular discrete systems

提出一种用于一般广义离散系统的严格真动态输出反馈H∞控制器设计方法。首先,构造辅助广义离散系统,给出该系统的状态反馈H∞控制器设计方法,在此基础上,用两组矩阵不等式给出使一般广义离散系统是允许的且满足H∞范数限制的控制器存在的充分条件,并给出了控制器的解析表达式。通过解这两组矩阵不等式,即可获得所需的控制器。控制器的可解性条件由系统的系数矩阵表达,因此不需要矩阵分解,可避免由矩阵分解产生的数值问题。仿真结果证实算法的有效性。

A method to design a strictly proper dynamic output feedback H∞ controller for common discrete singular system is given. First, an auxiliary singular discrete system is constructed and its state feedback H∞ controller is designed, and then by means of two groups of matrix inequalities, a sufficient condition for the existence of the dynamic output feedback H∞ controller is presented, such that the resulting closed-loop system is admissible with its transfer function satisfying H∞ norm constraint. By solving the two groups of matrix inequalities, the desired controller can be obtained. The condition for the solvability of the controllers is expressed by using the coefficient matrices of the whole system. The design procedure involves no decomposition of the system, which can avoid some numerical problems arising from the decomposition of matrices. A numerical example is given to demonstrate the application of the proposed method.