论文标题
当小收益遇到小阶段时
When Small Gain Meets Small Phase
论文作者
论文摘要
在本文中，我们研究了具有组合增益和相位信息的多输入多输出线性时间流动系统的反馈稳定性。首先，我们探索了一类所谓的易于控制的系统的稳定性条件，这些系统在低频范围内具有较小的相位，并且在高频下具有低增益。接下来，我们通过频率的增益和相结合扩展稳定性条件，基于将其混合的小增益和相位条件（称为小花瓶定理）获得。此外，通过基于Davis-Wielandt Shell的几何方法研究增益和相信息的融合。最后，出于有效的计算和控制器的合成目的，我们提出了一个有界和扇形的真实引理，该引理基于线性矩阵不等式的三重，对组合增益和相位属性进行了状态空间表征。
In this paper, we investigate the feedback stability of multiple-input multiple-output linear time-invariant systems with combined gain and phase information. To begin with, we explore the stability condition for a class of so-called easily controllable systems, which have small phase at low frequency ranges and low gain at high frequency. Next, we extend the stability condition via frequency-wise gain and phase combination, based on which a mixed small gain and phase condition with necessity, called a small vase theorem, is then obtained. Furthermore, the fusion of gain and phase information is investigated by a geometric approach based on the Davis-Wielandt shell. Finally, for the purpose of efficient computation and controller synthesis, we present a bounded & sectored real lemma, which gives state-space characterization of combined gain and phase properties based on a triple of linear matrix inequalities.
