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A Homology Theory for Hybrid Systems: Hybrid Homology

Summary: A Homology Theory for Hybrid Systems:
Hybrid Homology
Aaron D. Ames and Shankar Sastry
Department of Electrical Engineering and Computer Science,
University of California at Berkeley,
Berkeley, CA 94720
{adames, sastry}@eecs.berkeley.edu
Abstract. By transferring the theory of hybrid systems to a categorical
framework, it is possible to develop a homology theory for hybrid sys-
tems: hybrid homology. This is achieved by considering the underlying
"space" of a hybrid system--its hybrid space or H-space. The homotopy
colimit can be applied to this H-space to obtain a single topological space;
the hybrid homology of an H-space is the homology of this space. The
result is a spectral sequence converging to the hybrid homology of an
H-space, providing a concrete way to compute this homology. Moreover,
the hybrid homology of the H-space underlying a hybrid system gives
useful information about the behavior of this system: the vanishing of
the first hybrid homology of this H-space--when it is contractible and
finite--implies that this hybrid system is not Zeno.
1 Introduction


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


Collections: Engineering