Citation
Aaron Ames, Alessandro Abate, Shankar Sastry. "Sufficient Conditions for the Existence of Zeno Behavior". IEEE Conference on Decision and Control, December, 2005.

Abstract
In this paper, sufficient conditions for the existence of Zeno behavior in a class of hybrid systems are given; these are the first sufficient conditions on Zeno of which the authors are aware for hybrid systems with nontrivial dynamics. This is achieved by considering a class of hybrid systems termed {\em diagonal first quadrant (DFQ) hybrid systems}. When the underlying graph of a DFQ hybrid system has a cycle, we can construct an infinite execution for this system when the vector fields on each domain satisfy certain assumptions. To this execution, we can associate a single discrete time dynamical system that describes its continuous evolution. Therefore, we reduce the study of executions of DFQ hybrid systems to the study of a single discrete time dynamical system. We obtain sufficient conditions for the existence of Zeno by determining when this discrete time dynamical system is exponentially stable.

Electronic downloads

• AmesCDC2005.pdf · application/pdf · 628 kbytes

• HTML

  Aaron Ames, Alessandro Abate, Shankar Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/131.html"
  >Sufficient Conditions for the Existence of Zeno
  Behavior</a>, IEEE Conference on Decision and Control,
  December, 2005.

• Plain text

  Aaron Ames, Alessandro Abate, Shankar Sastry.
  "Sufficient Conditions for the Existence of Zeno
  Behavior". IEEE Conference on Decision and Control,
  December, 2005.

• BibTeX

  @inproceedings{AmesAbateSastry05_SufficientConditionsForExistenceOfZenoBehavior,
      author = {Aaron Ames and Alessandro Abate and Shankar Sastry},
      title = {Sufficient Conditions for the Existence of Zeno
                Behavior},
      booktitle = {IEEE Conference on Decision and Control},
      month = {December},
      year = {2005},
      abstract = {In this paper, sufficient conditions for the
                existence of Zeno behavior in a class of hybrid
                systems are given; these are the first sufficient
                conditions on Zeno of which the authors are aware
                for hybrid systems with nontrivial dynamics. This
                is achieved by considering a class of hybrid
                systems termed {\em diagonal first quadrant (DFQ)
                hybrid systems}. When the underlying graph of a
                DFQ hybrid system has a cycle, we can construct an
                infinite execution for this system when the vector
                fields on each domain satisfy certain assumptions.
                To this execution, we can associate a single
                discrete time dynamical system that describes its
                continuous evolution. Therefore, we reduce the
                study of executions of DFQ hybrid systems to the
                study of a single discrete time dynamical system.
                We obtain sufficient conditions for the existence
                of Zeno by determining when this discrete time
                dynamical system is exponentially stable.},
      URL = {http://chess.eecs.berkeley.edu/pubs/131.html}
  }
  

Posted by Aaron Ames on 15 May 2006.
For additional information, see the Publications FAQ or contact webmaster at chess eecs berkeley edu.