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 functionon 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.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

In this study, the theory of negative imaginary (NI) systems is extended to a nonlinear framework using a frequency-domain approach. The extended notion is characterized through finite-frequency integration over a kernel function and bounded input-output signal pairs. The feedback stability of the proposed nonlinear NI systems is established based on integral quadratic constraints.