Work

On phase in scaled graphs

Year: 2025

Type: conference-paper

Abstract: The scaled graph has been introduced recently as a nonlinear extension of the classical Nyquist plot for linear time-invariant systems. In this paper, we introduce a modified definition for the scaled graph, termed the signed scaled graph (SSG), in which the phase component is characterized by making use of the Hilbert transform. Whereas the original definition of the scaled graph uses unsigned phase angles, the new definition has signed phase angles which ensures the possibility to differentiate between phase-lead and phase-lag properties in a system. Making such distinction is important from both an analysis and a synthesis perspective, and helps in providing tighter stability estimates of feedback interconnections. We show how the proposed SSG leads to intuitive characterizations of positive real and negative imaginary nonlinear systems, and present various interconnection results. We showcase the effectiveness of our results through a motivating example.

Source: Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes

DOI: 10.1109/cdc57313.2025.11312812

Authors: Sebastiaan van den Eijnden, Chao Chen, Koen Scheres, Thomas Chaffey, Alexander Lanzon

Institutions: Eindhoven University of Technology, University of Manchester, The University of Sydney, KU Leuven

Language: English

Topic: Stability and Control of Uncertain Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: European Research Council

OpenAlex ID: W7123355809

FWCI: 2.289

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Cited by: 1

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