Exact Instability Margin Analysis and Minimum-Norm Strong Stabilization—Phase Change Rate Maximization

• 成果类型: Article
• 署名作者: Hara, Shinji; Kao, Chung-Yao; Khong, Sei Zhen; Iwasaki, Tetsuya; Hori, Yutaka
• 署名单位: Institute of Science Tokyo; Tokyo Institute of Technology; National Sun Yat Sen University; University of California System; University of California Los Angeles; Keio University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3324263
• 发表日期: 2024
• 页码: 2084-2099
• 关键词: Instability analysis; Nyquist criterion; phase change rate (PCR) maximization; Robust control; strong stabilization

摘要

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 -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.