Feedback Stability Analysis via Frequency Dependent Constraints

• 成果类型: Article
• 署名作者: Khong, Sei Zhen; Lanzon, Alexander
• 署名单位: National Sun Yat Sen University; University of Manchester
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3457432
• 发表日期: 2025
• 页码: 1228-1235
• 关键词: Stability criteria; Transfer functions; Linear systems; Time-frequency analysis; Sensor phenomena and characterization; Mechanical sensors; Linear matrix inequalities; Feedback stability; frequency dependent inequalities; integral quadratic constraints (IQCs); Iwasaki-Hara lemma

摘要

We establish robust stability of feedback interconnections of linear time-invariant systems with potentially marginally stable open-loop poles via frequency-varying quadratic constraints. These constraints may be used to characterise numerous system properties, such as small-gain, passivity, negative imaginariness, and their weighted variants, that are manifested on different band-limited frequencies. Such systems arise in practical mechanical settings where force actuators and displacement/velocity sensors are not colocated. We demonstrate that frequency-limited system properties may be characterised using the powerful Iwasaki-Hara lemma in terms of convex feasibility problems involving linear matrix inequalities, thereby complementing the utility of the Iwasaki-Hara lemma for robust feedback stability analysis involving mixed system properties on the frequency axis.