2021/03/25 by Thomas Chaffey, Chaffey, Thomas, Fulvio Forni +3 · 4 citations
Computer Science · Engineering · Mathematics · #47H05 #93C10 #93C80 #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering #math.OC #msc:47H05 #msc:93C10 #msc:93C80
paper · pdf · doi:10.48550/arxiv.2103.13971
Accepted to the 2021 IEEE Conference on Decision and Control
arxiv created 2021/10/07 · arxiv updated 2021/10/08
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 L2 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.