Continuous limit in dynamics with choice

Lev Kapitanski, Sanja Živanović Gonzalez

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We are interested in time evolution of systems that switch their modes of operation at discrete moments of time. The intervals between switching may, in general, vary. The number of modes may be finite or infinite. The mathematical setting for such systems is variable time step dynamics with choice. We have used this setting previously to study the long term behavior of such systems. In this paper, we define and study the continuous time dynamics whose trajectories are limits of trajectories of discrete systems as time step goes to zero. The limit dynamics is multivalued. In the special case of a switched system,when the dynamics is generated by switching between solutions of a finite number of systems of ODEs, we show that our continuous limit solution set coincides with the solution set of the relaxed differential inclusion.

Original languageEnglish (US)
Title of host publicationDifference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012
PublisherSpringer New York LLC
Number of pages30
ISBN (Print)9783662529263
StatePublished - 2016
Event18th International Conference on Difference Equations and Applications, ICDEA 2012 - Barcelona, Spain
Duration: Jul 23 2012Jul 27 2012


Other18th International Conference on Difference Equations and Applications, ICDEA 2012


  • Differential inclusions
  • Switched systems
  • Symbolic dynamics

ASJC Scopus subject areas

  • Mathematics(all)


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