 
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 systemits hybrid space or Hspace. The homotopy
colimit can be applied to this Hspace to obtain a single topological space;
the hybrid homology of an Hspace is the homology of this space. The
result is a spectral sequence converging to the hybrid homology of an
Hspace, providing a concrete way to compute this homology. Moreover,
the hybrid homology of the Hspace underlying a hybrid system gives
useful information about the behavior of this system: the vanishing of
the first hybrid homology of this Hspacewhen it is contractible and
finiteimplies that this hybrid system is not Zeno.
1 Introduction
