A homology theory for hybrid systems: Hybrid homology

Abstract

By transferring the theory of hybrid systems to a categorical framework, it is possible to develop a homology theory for hybrid systems: 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. © Springer-Verlag Berlin Heidelberg 2005.