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SUMMARY:Controllability and stabilizability of piecewise affine dynamical 
 systems - Kanat Camlibel\, University of Groningen
DTSTART:20161110T140000Z
DTEND:20161110T150000Z
UID:TALK68249@talks.cam.ac.uk
CONTACT:Tim Hughes
DESCRIPTION:Being one of the most fundamental concepts of systems and cont
 rol theory\, the controllability concept has been extensively studied\, ev
 er since conceived by Kalman\, in various contexts including linear system
 s\, nonlinear systems\, infinite-dimensional systems\, positive systems\, 
 switching systems\, hybrid systems\, and behavioral systems. Easily verifi
 able tests for global controllability have been hard to obtain with the ex
 ception of the classical results on finite-dimensional linear systems. In 
 fact\, even in the framework of smooth nonlinear systems\, results on cont
 rollability are local in nature and there is no hope to come up with gener
 al algebraic characterizations of global controllability. Indeed\, the pro
 blem of characterizing controllability for some classes of systems fall in
 to the most undesirable category of problems from computational complexity
  point of view\, namely undecidable problems. A remarkable example of such
  system classes is the so-called sign-systems which are the simplest insta
 nces of piecewise affine dynamical systems.\n\nA piecewise affine dynamica
 l system is a finite-dimensional nonlinear input/state/output dynamical sy
 stem with the distinguishing feature that the functions representing the s
 ystems differential equations are piecewise affine functions. Any piecewis
 e affine system can be considered as a collection of ordinary finite-dimen
 sional linear input/state/output systems\, together with a partition of th
 e product of the state space and input space into polyhedral regions. Each
  of these regions is associated with one particular linear system from the
  collection. Depending on the region in which the state and input vector a
 re contained at a certain time\, the dynamics is governed by the linear sy
 stem associated with that region. Thus\, the dynamics switches if the stat
 e-input vector changes from one polyhedral region to another. Any piecewis
 e affine systems is therefore also a hybrid system\, i.e.\, a dynamical sy
 stem whose time evolution is governed both by continuous as well as discre
 te dynamics.\n\nIn this talk\, we investigate controllability and stabiliz
 ability conditions for continuous piecewise affine dynamical systems. Alth
 ough every piecewise affine system is a nonlinear system\, none of the exi
 sting results for smooth nonlinear systems can be applied to piecewise aff
 ine systems because of the lack of smoothness. The main results of this ta
 lk are algebraic necessary and sufficient conditions for controllability a
 nd stabilizability of continuous piecewise affine systems. These condition
 s are much akin to classical Popov-Belevitch-Hautus controllability/stabil
 izability conditions.
LOCATION:Cambridge University Engineering Department\, LR4
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