论文标题
确切的不稳定性边缘分析和最小值强稳定 - 相变率最大化 -
Exact Instability Margin Analysis and Minimum-Norm Strong Stabilization -- phase change rate maximization --
论文作者
论文摘要
本文涉及一个新的优化问题，即单输入单输出线性时间不变系统的名为“相变率最大化”。该问题涉及两个控制问题，即针对稳定扰动和最小值稳定的强大不稳定性分析。我们将称为“鲁棒不稳定性半径（RIR）”的不稳定性余量的索引定义为稳定稳定扰动的最小$ h_ \ infty $ norm，它稳定了给定的不稳定系统。本文有两个主要贡献。首先表明，通过小增益条件找到确切的RIR的问题可以转变为最大化峰值频率下使用相位约束的相变率的问题。然后，我们表明，最大值是通过常数或一阶的全通函数来实现的，并得出条件，根据相变率，RIR可以精确地表征RIR。提供了两个实际应用来说明我们结果的实用性。
This paper 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 $H_\infty$-norm of a stable perturbation that stabilizes a given unstable system. This paper 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.
