Computing the Hard Scaled Relative Graph of LTI Systems
Julius P. J. Krebbekx, Eder Baron-Prada, Roland T\'oth, Amritam Das
TL;DR
This paper introduces a systematic computational approach to exactly compute the hard Scaled Relative Graphs (SRGs) of potentially unstable LTI systems, enhancing frequency-domain analysis of feedback loops.
Contribution
It develops a novel method for exact computation of hard SRGs for unstable LTI systems, including those with integrators, and explores their connection to the Nyquist criterion.
Findings
Exact computation method for hard SRGs of unstable LTI systems
Connection established between hard SRGs and Nyquist criterion
Demonstrations on multiple example systems
Abstract
Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems, where Linear Time-Invariant (LTI) systems are the fundamental building block. To analyze feedback loops with unstable LTI components, the hard SRG is required, since it aptly captures the input/output behavior on the extended space. In this paper, we develop a systematic computational method to exactly compute the hard SRG of LTI systems, which may be unstable and contain integrators. We also study its connection to the Nyquist criterion, including the multivariable case, and demonstrate our method on several examples.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsControl Systems and Identification · Model Reduction and Neural Networks · Stability and Control of Uncertain Systems