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Graphical Dominance Analysis for Linear Systems: A Frequency-Domain Approach

Published: April 19, 2025 | arXiv ID: 2504.14394v1

By: Chao Chen, Thomas Chaffey, Rodolphe Sepulchre

Potential Business Impact:

Helps engineers understand complex machine stability.

Business Areas:
Data Visualization Data and Analytics, Design, Information Technology, Software

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 results characterize sufficient conditions for quantifying the dominance of a closed-loop system based upon separation of scaled graphs of two open-loop systems in a frequency-wise manner. The results reconcile existing small gain, small phase and passivity theorems for feedback dominance analysis.

Country of Origin
🇦🇺 🇧🇪 🇬🇧 United Kingdom, Belgium, Australia

Page Count
8 pages

Category
Electrical Engineering and Systems Science:
Systems and Control