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SUMMARY:Positivity\, Monotonicity\, and Consensus on Lie Groups - Cyrus Mo
 stajeran\, University of Cambridge
DTSTART:20170216T140000Z
DTEND:20170216T150000Z
UID:TALK70774@talks.cam.ac.uk
CONTACT:Tim Hughes
DESCRIPTION:A dynamical system is said to be differentially positive if it
 s linearization along trajectories is positive in the sense that it infini
 tesimally contracts a smooth cone field. The property can be thought of as
  a generalization of monotonicity\, which is differential positivity in a 
 linear space with respect to a constant cone field. In this talk we consid
 er differentially positive systems defined on Lie groups and outline the m
 athematical framework for studying differential positivity with respect to
  invariant cone fields. We motivate the use of this analysis framework wit
 h examples from nonlinear consensus theory. We also introduce a generalize
 d notion of differential positivity with respect to an extended notion of 
 cone fields of higher rank k>=2. This provides the basis for a generalizat
 ion of differential Perron-Frobenius theory\, whereby the Perron-Frobenius
  vector field which shapes 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
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