Citation
Aaron Ames, Alessandro Abate, Shankar Sastry. "Sufficient Conditions for the Existence of Zeno Behavior in Nonlinear Hybrid Systems via Constant Approximations". 46th IEEE Conference on Decision and Control and European Control, 4033-4038, December, 2007.

Abstract
The existence of Zeno behavior in hybrid systems is related to a certain type of equilibria, termed Zeno equilibria, that are invariant under the discrete, but not the continuous, dynamics of a hybrid system. In analogy to the standard procedure of linearizing a vector field at an equilibrium point to determine its stability, in this paper we study the local behavior of a hybrid system near a Zeno equilibrium point by considering the value of the vector field on each domain at this point, i.e., we consider constant approximations of nonlinear hybrid systems. By means of these constant approximations, we are able to derive conditions that simultaneously imply both the existence of Zeno behavior and the local exponential stability of a Zeno equilibrium point. Moreover, since these conditions are in terms of the value of the vector field on each domain at a point, they are remarkably easy to verify.

Electronic downloads

• http://hybrid.stanford.edu/~aabate/pubs.htm
• http://dx.doi.org/10.1109/CDC.2007.4434891%20

• HTML

  Aaron Ames, Alessandro Abate, Shankar Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/438.html"
  >Sufficient Conditions for the Existence of Zeno Behavior
  in Nonlinear Hybrid Systems via Constant
  Approximations</a>, 46th IEEE Conference on Decision
  and Control and European Control, 4033-4038, December, 2007.

• Plain text

  Aaron Ames, Alessandro Abate, Shankar Sastry.
  "Sufficient Conditions for the Existence of Zeno
  Behavior in Nonlinear Hybrid Systems via Constant
  Approximations". 46th IEEE Conference on Decision and
  Control and European Control, 4033-4038, December, 2007.

• BibTeX

  @inproceedings{AmesAbateSastry07_SufficientConditionsForExistenceOfZenoBehaviorInNonlinear,
      author = {Aaron Ames and Alessandro Abate and Shankar Sastry},
      title = {Sufficient Conditions for the Existence of Zeno
                Behavior in Nonlinear Hybrid Systems via Constant
                Approximations},
      booktitle = {46th IEEE Conference on Decision and Control and
                European Control},
      pages = {4033-4038},
      month = {December},
      year = {2007},
      abstract = {The existence of Zeno behavior in hybrid systems
                is related to a certain type of equilibria, termed
                Zeno equilibria, that are invariant under the
                discrete, but not the continuous, dynamics of a
                hybrid system. In analogy to the standard
                procedure of linearizing a vector field at an
                equilibrium point to determine its stability, in
                this paper we study the local behavior of a hybrid
                system near a Zeno equilibrium point by
                considering the value of the vector field on each
                domain at this point, i.e., we consider constant
                approximations of nonlinear hybrid systems. By
                means of these constant approximations, we are
                able to derive conditions that simultaneously
                imply both the existence of Zeno behavior and the
                local exponential stability of a Zeno equilibrium
                point. Moreover, since these conditions are in
                terms of the value of the vector field on each
                domain at a point, they are remarkably easy to
                verify.},
      URL = {http://chess.eecs.berkeley.edu/pubs/438.html}
  }
  

Posted by Alessandro Abate on 16 Jun 2008.
Groups: chess
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