Scaled relative graphs for system analysis
Abstract
Scaled relative graphs were recently introduced to analyze the convergence of optimization algorithms using two dimensional Euclidean geometry. In this paper, we connect scaled relative graphs to the classical theory of input/output systems. It is shown that the Nyquist diagram of an LTI system on $L_2$ is the convex hull of its scaled relative graph under a particular change of coordinates. The SRG may be used to visualize approximations of static nonlinearities such as the describing function and quadratic constraints, allowing system properties to be verified or disproved. Interconnections of systems correspond to graphical manipulations of their SRGs. This is used to provide a simple, graphical proof of the classical incremental passivity theorem.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2103.13971
 Bibcode:
 2021arXiv210313971C
 Keywords:

 Electrical Engineering and Systems Science  Systems and Control;
 Mathematics  Optimization and Control;
 93C10;
 93C80;
 47H05
 EPrint:
 Accepted to the 2021 IEEE Conference on Decision and Control