离散对象的降阶H_∞控制器设计

Design of reduced-order H_∞ controllers for discrete-time plants

基于LMI方法,考虑了离散对象的阶数不超过广义对象阶的降阶H_∞控制器存在性问题。通过3LMIS可解性条件的等价变换,给出了一个降阶控制器的上界。该上界可适用于奇异和非奇异对象两种情形,且在奇异情形不为已有结果蕴涵。证明是构造性的,当降阶控制器存在时,可以设计出这种控制器。最后给出了两个简单的算例。

The existence of reduced-order H∞ controllers with order not greater than that of generalized plants was studied, based on LMI for discrete-time plants. An upper bound of order for the controllers was obtained via equivalent 3LMIs, and was applicable to both singular and non-singular plants. Moreover, the bound was not implied by the previous one for singular plants. Finally, two examples were given to show the feasibility of the method.