Dynamical Systems Revisited: Hybrid Systems with Zeno Executions

  • Authors:
  • Jun Zhang;Karl Henrik Johansson;John Lygeros;Shankar Sastry

  • Affiliations:
  • -;-;-;-

  • Venue:
  • HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
  • Year:
  • 2000

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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.