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Stability of hybrid systems

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Hybrid Systems III (HS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1066))

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Abstract

Hybrid systems combine discrete and continuous behavior. We study properties of trajectories of a rectangular hybrid system in which the discrete state goes through a loop. This system is viable if there exists an infinite trajectory starting from some state. We show that the system is viable if and only if it has a limit cycle or fixed point. The set of fixed points is a polyhedron. The viability kernel may not be a polyhedron. However, under a “controllability” condition, the viability kernel is a polyhedron.

Research supported by NSF Grant ECS9417370. The authors are grateful to Mireille Broucke for posing the questions addressed here, and to Anuj Puri for discussion.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, University of California at Berkeley, 94720, Berkeley, California

    Mikhail Kourjanski & Pravin Varaiya

Authors
  1. Mikhail Kourjanski
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  2. Pravin Varaiya
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Rajeev Alur Thomas A. Henzinger Eduardo D. Sontag

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© 1996 Springer-Verlag Berlin Heidelberg

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Kourjanski, M., Varaiya, P. (1996). Stability of hybrid systems. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds) Hybrid Systems III. HS 1995. Lecture Notes in Computer Science, vol 1066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020964

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  • DOI: https://doi.org/10.1007/BFb0020964

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61155-4

  • Online ISBN: 978-3-540-68334-6

  • eBook Packages: Springer Book Archive

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