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International Workshop on Hybrid Systems: Computation and Control

HSCC 2000: Hybrid Systems: Computation and Control pp 451–464Cite as

Dynamical Systems Revisited: Hybrid Systems with Zeno Executions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1790))

Abstract

Results from classical dynamical systems are generalized to hybrid dynamical systems. The concept of ω limit set is introduced for hybrid systems and is used to prove new results on invariant sets and stability, where Zeno and non-Zeno hybrid systems can be treated within the same framework. As an example, LaSalle’s Invariance Principle is extended to hybrid systems. Zeno hybrid systems are discussed in detail. The ω limit set of a Zeno execution is characterized for classes of hybrid systems

This work was supported by ARO under the MURI grant DAAH04-96-1-0341, the Swedish Foundation for International Cooperation in Research and Higher Education, Telefonaktiebolaget LM Ericsson’s Foundation, ONR under grant N00014-97-1-0946, and DARPA under contract F33615-98-C-3614.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, 94720-1770

    Jun Zhang, Karl Henrik Johansson, John Lygeros & Shankar Sastry

Authors
  1. Jun Zhang
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  2. Karl Henrik Johansson
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  3. John Lygeros
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  4. Shankar Sastry
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Editor information

Editors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Nancy Lynch

  2. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15235, USA

    Bruce H. Krogh

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© 2000 Springer-Verlag Berlin Heidelberg

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Zhang, J., Johansson, K.H., Lygeros, J., Sastry, S. (2000). Dynamical Systems Revisited: Hybrid Systems with Zeno Executions. In: Lynch, N., Krogh, B.H. (eds) Hybrid Systems: Computation and Control. HSCC 2000. Lecture Notes in Computer Science, vol 1790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46430-1_37

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  • DOI: https://doi.org/10.1007/3-540-46430-1_37

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67259-3

  • Online ISBN: 978-3-540-46430-3

  • eBook Packages: Springer Book Archive

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