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Sufficient Conditions for the Existence of Zeno Behavior Aaron D. Ames, Alessandro Abate and Shankar Sastry
 

Summary: Sufficient Conditions for the Existence of Zeno Behavior
Aaron D. Ames, Alessandro Abate and Shankar Sastry
Department of Electrical Engineering and Computer Sciences
University of California, Berkeley
Berkeley, CA 94720
{adames,aabate,sastry}@eecs.berkeley.edu
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 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

  

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

 

Collections: Engineering