Argument Principle and Integral Relations: Hidden Links and Generalized Forms

• 成果类型: Article
• 署名作者: Xu, Yong; Chen, Gang; Chen, Jie; Qiu, Li
• 署名单位: Guangdong University of Technology; University of California System; University of California Riverside; City University of Hong Kong; Hong Kong University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3159565
• 发表日期: 2023
• 页码: 1831-1838
• 关键词: Argument principle; Bode/Poisson integral relations; performance limitation

摘要

This article studies Bode/Poisson type sensitivity and complementary sensitivity integral relations for linear, time-invariant feedback control systems. We call for attention to a seemingly unnoticed link between the well-known argument principle and Bode/Poisson integral relations. In this respect, a generalized version of the argument principle is developed, under which it is shown that various Bode/Poisson type integral relations can be unified, and new integral relations can be derived. The new and classical integral relations together provide useful insights for analyzing control design limitations and tradeoffs.