具有乘法式摄动的广义系统H_∞控制器设计

H_∞ controller design with the disturbance of multiplication for descriptor systems

研究基于观测器的广义系统H_∞控制器设计问题。对所给的广义系统模型设计具有乘法式摄动的广义控制器,并给出H_∞控制器的定义。用广义代数Riccati不等式(generalizedalgebraicriccatiinequality,GARI)和线性矩阵不等式(linearmatrixinequality,LMI)两种方法,给出闭环广义系统存在具有乘法式摄动的H_∞控制器的3个等价命题,同时也给出了具有乘法式摄动的H_∞控制器的两种设计方法,并对这两种设计方法进行了比较。最后用一个数值例子演示了设计过程并说明此方法的有效性。

The problem of H_∞ controller design for descriptor systems based on observer is discussed. Firstly, a generalized controller with the disturbance of multiplication is designed for the given model of descriptor system and the definition of H_∞ controller is proposed. Secondly, three equivalent statements are obtained by GARI and LMI. These conditions guarantee that there exists H_∞ controller with the disturbance of multiplication for closed-loop descriptor systems. Meanwhile, two H_∞ controller design methods are obtained. These two design methods are compared. Finally, a numerical example is given to illustrate the design procedures and their effectiveness.