Stability results for MIMO LTI systems via Scaled Relative Graphs

2025/03/17 by Baron-Prada, Eder, Anta, Adolfo, Padoan, Alberto +1 · 4 citations
#FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2503.13583

Abstract

This paper proposes a new approach for stability analysis of multi-input, multi-output (MIMO) feedback systems through Scaled Relative Graphs (SRGs). Unlike traditional methods, such as the Generalized Nyquist Criterion (GNC), which relies on a coupled analysis that requires the multiplication of models, our approach enables the evaluation of system stability in a decoupled fashion and provides an intuitive, visual representation of system behavior. Our results provide conditions for certifying the stability of feedback MIMO Linear Time-Invariant (LTI) systems.

Cited by

• Scaled relative graphs for pairs of operators beyond classical monotonicity
• Computable Characterisations of Scaled Relative Graphs of Closed Operators
• The Phantom of Davis-Wielandt Shell: A Unified Framework for Graphical Stability Analysis of MIMO LTI Systems
• A Dissipativity Framework for Constructing Scaled Graphs

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