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SUMMARY:Graphical Nonlinear System Analysis - Tom Chaffey\, University of 
 Cambridge
DTSTART:20210617T130000Z
DTEND:20210617T140000Z
UID:TALK161089@talks.cam.ac.uk
CONTACT:Thiago Burghi
DESCRIPTION:Scaled relative graphs (SRGs) were recently introduced by Ryu\
 , Hannah and Yin to analyze the convergence of optimization algorithms usi
 ng two dimensional Euclidean geometry. In this seminar\, I’ll show how t
 he SRG can be used to study incremental input/output properties of feedbac
 k systems. The SRG of an LTI transfer function is the convex hull of its N
 yquist diagram under a particular change of coordinates. The SRG may be pl
 otted or approximated for arbitrary nonlinear operators\, and allows class
 ical Nyquist techniques to be applied to nonlinear systems. System interco
 nnection corresponds to graphical manipulations of the systems’ SRGs. I 
 will give a generalization of the Nyquist criterion for stable systems\, w
 here the Nyquist diagram and the point −1 are replaced by SRGs of two fe
 edback-interconnected nonlinear operators. This theorem encompasses the in
 cremental small gain and passivity theorems\, and mixed small gain/passivi
 ty theorems. The distance between the two SRGs is a nonlinear stability ma
 rgin\, and is the reciprocal of the incremental gain of the feedback syste
 m. SRGs can be over-approximated based on system properties such as passiv
 ity and incremental gain\, and can be plotted precisely for some static no
 nlinearities. I will provide an analytical calculation of the saturation f
 unction\, and show how SRG analysis of Lur’e systems gives advantages ov
 er classical tools ranging from the circle criterion to IQC analysis.\n\nZ
 oom link:\nhttps://zoom.us/j/96507147724
LOCATION:Online (Zoom)
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