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Retrospect and prospect on integration of gain and phase for feedback stability analysis
DiZhao1,LiQiu2,3
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(1 Department of Control Science and Engineering & Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai 201804, China;2 Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China; 3 Guangzhou HKUST Fok Ying Tung Research Insititute, Nansha District, Guangzhou 511458, Guangdong, China)
摘要:
In this paper, we review existing approaches to integrating small gain and small phase analysis for feedback stability of dynamical systems, and give a brief outlook for possible future directions in exploring this topic. Small gain analysis has been very successful and popular in control theory since 1960s, while the small phase analysis for multiple-input-multiple-output systems has not been well understood until recently and is now gradually taking shape. Nevertheless, there have been attempts to analyzing feedback stability via the integration of gain and phase information over decades, including the combination of small gain with positive realness as well as that with negative imaginariness. Such combinations can be subsumed into a recently proposed framework for gain-phase integration, which brings in new geometrical methods and also sheds new lights on several future directions.
关键词:  Small gain · Small phase · Passivity · Positive real · Negative imaginary · Davis-Wielandt shell
DOI:https://doi.org/10.1007/s11768-022-00119-6
基金项目:This work was supported in part by the Shenzhen Science and Technology Innovation Committee, China (SGDX20201103094600006), by the Foshan-HKUST Projects Program (FSUST20-FYTRI12F), by the National Natural Science Foundation of China (62103303), and by the Shanghai Municipal Science and Technology, China Major Project (2021SHZDZX0100).
Retrospect and prospect on integration of gain and phase for feedback stability analysis
Di Zhao1,Li Qiu2,3
(1 Department of Control Science and Engineering & Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai 201804, China;2 Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China; 3 Guangzhou HKUST Fok Ying Tung Research Insititute, Nansha District, Guangzhou 511458, Guangdong, China)
Abstract:
In this paper, we review existing approaches to integrating small gain and small phase analysis for feedback stability of dynamical systems, and give a brief outlook for possible future directions in exploring this topic. Small gain analysis has been very successful and popular in control theory since 1960s, while the small phase analysis for multiple-input-multiple-output systems has not been well understood until recently and is now gradually taking shape. Nevertheless, there have been attempts to analyzing feedback stability via the integration of gain and phase information over decades, including the combination of small gain with positive realness as well as that with negative imaginariness. Such combinations can be subsumed into a recently proposed framework for gain-phase integration, which brings in new geometrical methods and also sheds new lights on several future directions.
Key words:  Small gain · Small phase · Passivity · Positive real · Negative imaginary · Davis-Wielandt shell