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Switching systems and periodicity

Part of the Lecture Notes in Mathematics book series (LNM,volume 1394)

Abstract

We consider a class of bimodal systems which alternate modes on hitting ‘switching surfaces’: the canonical model is a physical thermostat. A sufficient condition is obtained for the existence of periodic solutions. The significance for this theory of certain anomalous points on the switching surface is shown by an example with no periodic solutions. Further discussion is presented for the important case of linear switching systems, including a new existence theorem.

Keywords

  • Periodic Solution
  • Global Attractor
  • Alternate Mode
  • Impulse Response Function
  • Switching System

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This research has been partially supported by the Air Force Office of Scientific Research under grants #AFOSR-87-0190 and #AFOSR-87-0350.

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© 1989 Springer-Verlag

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Seidman, T.I. (1989). Switching systems and periodicity. In: Gill, T.L., Zachary, W.W. (eds) Nonlinear Semigroups, Partial Differential Equations and Attractors. Lecture Notes in Mathematics, vol 1394. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086761

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  • DOI: https://doi.org/10.1007/BFb0086761

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51594-4

  • Online ISBN: 978-3-540-46679-6

  • eBook Packages: Springer Book Archive