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A Stability Criterion for Stochastic Hybrid Systems

Summary: A Stability Criterion for
Stochastic Hybrid Systems
Alessandro Abate, Ling Shi, Slobodan N. Simi´c and S. Shankar Sastry
Department of Electrical Engineering and Computer Sciences
University of California at Berkeley
Berkeley, CA 94720
Tel: (510) 643-4867, Fax: (510) 642-1341
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 Sys-
tems 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.


Source: Abate, Alessandro - Faculty of Mechanical, Maritime and Materials Engineering, Technische Universiteit Delft


Collections: Engineering