The singular control problem with dynamic measurement feedback
The singular control problem with dynamic measurement feedback
复制标题
动态测量反馈的奇异控制问题
DOI：
10.1137/0329009
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发表时间：
1991
影响因子：
2.2
通讯作者：
A. Stoorvogel
中科院分区：
文献类型：
--
作者：
A. Stoorvogel
本文研究具有测量反馈的$H_\infty $问题。问题是要找到一个动态反馈从测量输出到控制输入，使闭环系统有一个$H_\infty $范数严格小于一些先验给定的界$\gamma $，使闭环系统是内部稳定的。给出了这种反馈存在的充分必要条件。唯一必须做的假设是两个子系统的虚轴上没有不变零点。与最近的出版物相反，没有对工厂的直接馈通矩阵进行假设。结果表明，该问题可以归结为具有测量反馈和内部稳定性的几乎干扰解耦问题，即，我们可以使$H_\infty $范数任意小的问题。
This paper is concerned with the $H_\infty $ problem with measurement feedback. The problem is to find a dynamic feedback from the measured output to the control input such that the closed-loop system has an $H_\infty $ norm strictly less than some a priori given bound $\gamma $ and such that the closed-loop system is internally stable. Necessary and sufficient conditions are given under which such a feedback exists. The only assumption that must be made is that there are no invariant zeros on the imaginary axis for two subsystems. Contrary to recent publications no assumptions are made on the direct feedthrough matrices of the plant. It turns out that this problem can be reduced to an almost disturbance decoupling problem with measurement feedback and internal stability, i.e., the problem in which we can make the $H_\infty $ norm arbitrarily small.