Exact Instability Margin Analysis and Minimum-Norm Strong Stabilization—Phase Change Rate Maximization
Exact Instability Margin Analysis and Minimum-Norm Strong Stabilization—Phase Change Rate Maximization
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精确的不稳定裕度分析和最小范数强稳定——相变率最大化
DOI：
10.1109/tac.2023.3324263
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发表时间：
2022
影响因子：
6.8
通讯作者：
Yutaka Hori
中科院分区：
文献类型：
--
作者：
S. Hara;Chung;Sei Zhen Khong;T. Iwasaki;Yutaka Hori
研究了单输入单输出线性定常系统的一个新的优化问题--相位变化率最大化问题。该问题涉及两个控制问题，即对稳定扰动的鲁棒不稳定性分析和最小范数强镇定。我们定义了一个指标的不稳定裕度称为“鲁棒不稳定半径（RIR）”作为最小的$\mathcal {H}_\infty$-范数的稳定扰动，稳定一个给定的不稳定系统。这篇文章有两个主要贡献。它首先表明，通过小增益条件找到确切的RIR的问题可以转化为最大化的相位变化率在峰值频率与相位约束的问题。然后，我们表明，最大值是通过一个常数或一阶全通函数和推导条件，在此条件下，RIR可以准确地表征，在相位变化率。两个实际的应用程序来说明我们的结果的效用。
This article is concerned with a new optimization problem named “phase change rate maximization” for single-input–single-output linear time-invariant systems. The problem relates to two control problems, namely robust instability analysis against stable perturbations and minimum-norm strong stabilization. We define an index of the instability margin called “robust instability radius (RIR)” as the smallest $\mathcal {H}_\infty$-norm of a stable perturbation that stabilizes a given unstable system. This article has two main contributions. It is first shown that the problem of finding the exact RIR via the small-gain condition can be transformed into the problem of maximizing the phase change rate at the peak frequency with a phase constraint. Then, we show that the maximum is attained by a constant or a first-order all-pass function and derive conditions, under which the RIR can be exactly characterized, in terms of the phase change rate. Two practical applications are provided to illustrate the utility of our results.
DOI：
--
发表时间：
2023
期刊：
IFAC World Congress
影响因子：
--
作者：
C.-Y. Kao, S. Hara
通讯作者：
C.-Y. Kao, S. Hara