16:00 - 17:00
Title: System analysis with scaled relative graphs
Abstract: Scaled relative graphs (SRGs) were recently introduced by Ryu, Hannah and Yin to analyze the convergence of optimisation algorithms using two dimensional Euclidean geometry. In this seminar, I’ll show how the SRG can be used to study incremental input/output properties of feedback systems. The SRG of an LTI transfer function is closely related to its Nyquist diagram. The SRG may be plotted or approximated for arbitrary nonlinear operators, and allows classical Nyquist techniques to be applied to nonlinear systems. I will give a generalisation of the Nyquist criterion for stable systems, where the Nyquist diagram and the point −1 are replaced by SRGs of two feedback-interconnected nonlinear operators. The distance between the two SRGs is a nonlinear stability margin, and is the reciprocal of the incremental gain of the feedback system. This theorem generalises a range of existing results, and has advantages over classical input/output techniques.