Graphical Dominance Analysis for Linear Systems: A Frequency-Domain Approach
Year: 2025
Type: conference-paper
Abstract: We propose a frequency-domain approach to dominance analysis for multi-input multi-output (MIMO) linear time-invariant systems. The dominance of a MIMO system is defined to be the number of its poles in the open right half-plane. Our approach is graphical: we define a frequency-wise notion of the recently-introduced scaled graph of a MIMO system plotted in a complex plane. The scaled graph provides a bound of the eigenloci of the system, which can be viewed as a robust MIMO extension of the classical Nyquist plot. Our main result characterizes sufficient conditions for quantifying the dominance of a closed-loop system based upon separation of the scaled graphs of two open-loop systems in a frequency-wise manner. The result reconciles existing small gain, small phase and passivity theorems for feedback dominance analysis.
Authors: Chao Chen, Thomas Chaffey, Rodolphe Sepulchre
Institutions: University of Manchester, The University of Sydney, KU Leuven
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: European Research Council
OpenAlex ID: W7123363146