H∞-control of differential-algebraic-equation systems
H∞-control of differential-algebraic-equation systems
复制标题
微分代数方程组的 H∞ 控制
DOI：
10.18419/opus-6900
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
F. Allgöwer
中科院分区：
文献类型：
--
作者：
A. Rehm;F. Allgöwer
本文讨论了高指数和非正则线性微分代数方程系统的 H∞ 控制。基于对一个系统进行索引的有界实数引理 (BRL) 的推广，所有以标准（即非描述符）状态空间形式求解 H∞ 控制问题的线性输出反馈控制器都可以通过双仿射矩阵不等式 (BMI) 来表征。在第二步中，同余变换和随后的变量变化表明，某些线性矩阵不等式 (LMI) 必须成立，才能获得 H∞ 控制问题的解。然而，这些条件还不够。解决 H∞ 控制问题的控制器存在的必要和充分条件被导出为与通过 BRL 的原始表征相比降阶的 BMI。通过一个简单的例子来说明该方法。
In this paper H∞ control of high index and non-regular linear differential-algebraic-equation systems is addressed. Based on a generalization of the bounded real lemma (BRL) to index one systems, all linear output feedback controllers in standard, ie non-descriptor, state space form solving the H∞ control problem can be characterized via biaffine matrix inequalities (BMIs). In a second step a congruence transformation and a subsequent change of variables show that certain linear matrix inequalities (LMIs) necessarily must hold in order to admit a solution of the H∞ control problem. However, these conditions are not sufficient. Necessary and sufficient conditions for the existence of a controller solving the H∞ control problem are derived as BMIs of reduced order compared to the original characterization via the BRL. The approach is illustrated by a simple example.