BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Differentially positive systems - Fulvio Forni\, University of Cam
 bridge
DTSTART:20140313T140000Z
DTEND:20140313T150000Z
UID:TALK50520@talks.cam.ac.uk
CONTACT:Tim Hughes
DESCRIPTION:The trajectories of a positive system leave a cone invariant. 
 Positive systems have a rich history both because of the relevance in appl
 ications (e.g.\, when modeling a behavior defined by positive variables) a
 nd because positivity significantly restricts the behavior\, leading to th
 e Perron-Frobenius theory. Motivated by the importance of positivity in li
 near system analysis\, the talk introduces and explores the concept of dif
 ferential positivity for nonlinear behaviors. Differential positivity mean
 s positivity of  the linearized system along any trajectory. We derive th
 e analog of  Perron-Frobenius theory in this generalized setup and explor
 e its consequences for the asymptotic behavior of the system. We show that
 \, under suitable conditions\, differential positivity strongly restricts 
 the asymptotic behavior and provides a novel analysis and design tool for 
 multistable or limit cycle behaviors.  The analysis of a simple bistable 
 model and of a nonlinear pendulum will illustrate the potential of the app
 roach.
LOCATION:Cambridge University Engineering Department\, LR3
END:VEVENT
END:VCALENDAR