线性系统的鲁棒特征结构配置

如何配置一个系统的特征结构使系统的条件指数最小化为1,从而使系统对参数摄动具有最好的鲁棒性是一个被忽略的问题.针对这一问题采用状态反馈, 以条件指数作为系统鲁棒性能指标,对线性系统提出了该问题的解存在的充分条件,又对满足充分条件的系统给出了相应的特征结构配置算法及控制器设计.该设计过程简单、实用, 并通过仿真验证了在参数摄动小于闭环系统主导极点实部的绝对值时,系统保持了鲁棒稳定性.

Robust eigenstructure assignment for a class of linear systems

It is seldom mentioned to minimize the condition number of a system to reach 1 by assigning the eigenstructure, such a system possesses the best robustness to the parameter perturbations.Based on the state feedback, taking the condition number of closed-loop system as the robustness criterion, sufficient conditions, the robustness for system parameter perturbations is optimized and derived. And the corresponding controller design is presented, which is simple and realistie. Finally, a numerical example has demonstrated that the close-loop system keeps robust stable using the proposed method when the parameter perturbations are retained within the distance from the minimal pole to imaginary axis.