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Characterization of Zeno Behavior in Hybrid Systems Using Homological Methods

Summary: Characterization of Zeno Behavior in Hybrid Systems Using
Homological Methods
Aaron D. Ames and Shankar Sastry
Department of Electrical Engineering and Computer Sciences
University of California at Berkeley
Berkeley, CA 94720
Abstract-- It is possible to associate to a hybrid system
a single topological space­its underlying topological space.
Simultaneously, every hybrid system has a graph as its
indexing object­its underlying graph. Here we discuss the
relationship between the underlying topological space of a
hybrid system, its underlying graph and Zeno behavior. When
each domain is contractible and the reset maps are homotopic
to the identity map, the homology of the underlying topological
space is isomorphic to the homology of the underlying graph;
the nonexistence of Zeno is implied when the first homology
is trivial. Moreover, the first homology is trivial when the null
space of the incidence matrix is trivial. The result is an easy
way to verify the nonexistence of Zeno behavior.


Source: Ames, Aaron - Department of Mechanical Engineering, Texas A&M University


Collections: Engineering