A frequency-domain approach to nonlinear negative imaginary systems analysis

In this study, we extend the theory of negative imaginary (NI) systems to a nonlinear framework using a frequency-domain approach. The extended notion is completely characterized via a finite-frequency integration over a “kernel function” on energy-bounded input and output signal pairs. The notion i...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 146; p. 110604
Main Authors Zhao, Di, Chen, Chao, Khong, Sei Zhen
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2022
Subjects
Counterclockwise dynamics
Frequency-domain analysis
Integral quadratic constraints
Negative imaginary systems
Nonlinear systems
Integral quadratic constraints
Negative imaginary systems
Frequency-domain analysis
Counterclockwise dynamics
Nonlinear systems
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Summary:In this study, we extend the theory of negative imaginary (NI) systems to a nonlinear framework using a frequency-domain approach. The extended notion is completely characterized via a finite-frequency integration over a “kernel function” on energy-bounded input and output signal pairs. The notion is closely related to and carefully contrasted with the well-studied extension of negative imaginariness — the theory of counterclockwise dynamics. Conditions for feedback stability of the proposed nonlinear NI systems are then developed based on the technique of integral quadratic constraints. Examples and simulations on feedback interconnections of typical nonlinear systems are provided to demonstrate the effectiveness.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2022.110604