LMI方法和μ综合方法设计鲁棒控制系统

μ-synthesis Method and LMI Design for Robust Control System

介绍了目前广泛使用求解H∞控制问题的LM I(线形矩阵不等式)方法和μ综合设计方法。由于H∞方法的设计框架导致了系统保守性并忽略了鲁棒性能设计而与H∞同时期发展的μ理论则考虑了结构化的不确定性问题,它不但能有效地、无保守性的判断“最坏情况”下摄动的影响,而且在存在不同表达形式的结构化的情况下,能分析控制系统的鲁棒稳定性和鲁棒性能问题。最后分析两种方法的关系并对两种方法进行了比较。

The paper introduce LMI method which is extensive used to solve H∞ control problem and μ - synthesis method. Because of the design configuration of H∞ method, the system is conservative and neglected the robust performance design. But μ theory considers the structured uncertainty problem which is developed at the same time with H∞ theory. μ theory not only effecdy and non - conservatively judges the effect of perturbation in the worst situation, but also analyses the robust stability and robust performance problem of the control system in the situation of existing different expression of structured problem. And the relation and difference of two methods is discussed in the end of the paper.