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Dynamical Systems Revisited: Hybrid Systems with Zeno Executions

  • Jun Zhang
  • Karl Henrik Johansson
  • John Lygeros
  • Shankar Sastry
Conference paper
Part of the Lecture Notes in Computer Science book series (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

Keywords

Hybrid System Continuous Part Discrete Transition Hybrid Automaton Hybrid Dynamical 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.

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References

  1. 1.
    M. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control, 43(4):475–482, April 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    M. Branicky, E. Dolginova, and N. Lynch. A toolbox for proving and maintaining hybrid specifications. In P. Antsaklis, W. Kohn, A. Nerode, and S. Sastry, editors, Hybrid Systems IV, number 1273 in LNCS, pages 18–30. Springer Verlag, 1997.CrossRefGoogle Scholar
  3. 3.
    K. X. He and M. D. Lemmon. Lyapunov stability of continuous-valued systems under the supervision of discrete-event transition systems. In Hybrid Systems: Computation and Control, volume 1386 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1998.Google Scholar
  4. 4.
    K. H. Johansson, M. Egerstedt, J. Lygeros, and S. Sastry. On the regularization of Zeno hybrid automata. Systems & Control Letters, 38:141–150, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    K. H. Johansson, J. Lygeros, S. Sastry, and M. Egerstedt. Simulation of Zeno hybrid automata. In IEEE Conference on Decision and Control, Phoenix, AZ, 1999.Google Scholar
  6. 6.
    M. D. Lemmon, K. X. He, and I Markovsky. Supervisory hybrid systems. IEEE Control Systems Magazine, 19(4):42–55, 1999.CrossRefGoogle Scholar
  7. 7.
    J. Lygeros, K. H. Johansson, S. Sastry, and M. Egerstedt. On the existence of executions of hybrid automata. In IEEE Conference on Decision and Control, Phoenix, AZ, 1999.Google Scholar
  8. 8.
    J. Lygeros, C. Tomlin, and S. Sastry. Controllers for reachability specifications for hybrid systems. Automatica, 35(3), March 1999.Google Scholar
  9. 9.
    A. S. Morse. Control using logic-based switching. In Alberto Isidori, editor, Trends in Control. A European Perspective, pages 69–113. Springer, 1995.Google Scholar
  10. 10.
    S. Sastry. Nonlinear Systems: Analysis, Stability, and Control. Springer-Verlag, New York, 1999.zbMATHGoogle Scholar
  11. 11.
    S Simić, K H Johansson, S Sastry, and J Lygeros. Towards a geometric theory of hybrid systems. In Hybrid Systems: Computation and Control, Pittsburgh, PA, 2000.Google Scholar
  12. 12.
    A. J. van der Schaft and J. M. Schumacher. Complementarity modeling of hybrid systems. IEEE Transactions on Automatic Control, 43(4):483–490, April 1998.zbMATHCrossRefGoogle Scholar
  13. 13.
    S. Wiggins. Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer-Verlag, New York, 1990.zbMATHGoogle Scholar
  14. 14.
    H. Ye, A. Michel, and L. Hou. Stability theory for hybrid dynamical systems. IEEE Transactions on Automatic Control, 43(4):461–474, April 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    J. Zhang. Dynamical systems revisited: Hybrid systems with Zeno executions. Master’s thesis, Dept of EECS, University of California, Berkeley, 1999Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jun Zhang
    • 1
  • Karl Henrik Johansson
    • 1
  • John Lygeros
    • 1
  • Shankar Sastry
    • 1
  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeley

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