Citation
A. Abate, L. Shi, S. Simic, S. Sastry. "A stability criterion for Stochastic Hybrid Systems". Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems, Leuven, Jul. 2004, January, 2004.

Abstract
This paper investigates the notion of stability for Stochastic Hybrid Systems. The uncertainty is introduced in the discrete jumps between the domains, as if we had an underlying Markov Chain. The jumps happen every fixed time T; moreover, a result is given for the case of probabilistic dwelling times inside each domain. Unlike the more classical Hybrid Systems setting, the guards here are time-related, rather than space-related. We shall focus on vector fields describing input-less dynamical systems. Clearly, the uncertainty intrinsic to the model forces to introduce a fairly new definition of stability, which can be related to the classical Lyapunov one though. Proofs and simulations for our results are provided, as well as a motivational example from finance.

Electronic downloads

• StabilityCriterionSHS.pdf · application/pdf · 407 kbytes

• HTML

  A. Abate, L. Shi, S. Simic, S. Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/104.html"
  >A stability criterion for Stochastic Hybrid
  Systems</a>, Proceedings of the 16th International
  Symposium on Mathematical Theory of Networks and Systems,
  Leuven, Jul. 2004, January, 2004.

• Plain text

  A. Abate, L. Shi, S. Simic, S. Sastry. "A stability
  criterion for Stochastic Hybrid Systems". Proceedings
  of the 16th International Symposium on Mathematical Theory
  of Networks and Systems, Leuven, Jul. 2004, January, 2004.

• BibTeX

  @inproceedings{AbateShiSimicSastry04_StabilityCriterionForStochasticHybridSystems,
      author = {A. Abate and L. Shi and S. Simic and S. Sastry},
      title = {A stability criterion for Stochastic Hybrid Systems},
      booktitle = {Proceedings of the 16th International Symposium on
                Mathematical Theory of Networks and Systems,
                Leuven, Jul. 2004},
      month = {January},
      year = {2004},
      abstract = {This paper investigates the notion of stability
                for Stochastic Hybrid Systems. The uncertainty is
                introduced in the discrete jumps between the
                domains, as if we had an underlying Markov Chain.
                The jumps happen every fixed time T; moreover, a
                result is given for the case of probabilistic
                dwelling times inside each domain. Unlike the more
                classical Hybrid Systems setting, the guards here
                are time-related, rather than space-related. We
                shall focus on vector fields describing input-less
                dynamical systems. Clearly, the uncertainty
                intrinsic to the model forces to introduce a
                fairly new definition of stability, which can be
                related to the classical Lyapunov one though.
                Proofs and simulations for our results are
                provided, as well as a motivational example from
                finance.},
      URL = {http://chess.eecs.berkeley.edu/pubs/104.html}
  }
  

Posted by Alessandro Abate on 15 May 2006.
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