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CATEGORIES:CUED Control Group Seminars
SUMMARY:Positivity\, Monotonicity\, and Consensus on Lie G
roups - Cyrus Mostajeran\, University of Cambridge
DTSTART;TZID=Europe/London:20170216T140000
DTEND;TZID=Europe/London:20170216T150000
UID:TALK70774AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/70774
DESCRIPTION:A dynamical system is said to be differentially po
sitive if its linearization along trajectories is
positive in the sense that it infinitesimally cont
racts a smooth cone field. The property can be tho
ught of as a generalization of monotonicity\, whic
h is differential positivity in a linear space wit
h respect to a constant cone field. In this talk w
e consider differentially positive systems defined
on Lie groups and outline the mathematical framew
ork for studying differential positivity with resp
ect to invariant cone fields. We motivate the use
of this analysis framework with examples from nonl
inear consensus theory. We also introduce a genera
lized notion of differential positivity with respe
ct to an extended notion of cone fields of higher
rank k>=2. This provides the basis for a generaliz
ation of differential Perron-Frobenius theory\, wh
ereby the Perron-Frobenius vector field which shap
es the one-dimensional attractors of a differentia
lly positive system is replaced by a distribution
of rank k which results in k-dimensional integral
submanifold attractors.
LOCATION:Cambridge University Engineering Department\, LR12
CONTACT:Tim Hughes
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