 
Summary: Affine Hybrid Systems
Aaron D. Ames and Shankar Sastry
University of California, Berkeley CA 94720, USA
{adames,sastry}@eecs.berkeley.edu
Abstract. Affine hybrid systems are hybrid systems in which the dis
crete domains are affine sets and the transition maps between discrete
domains are affine transformations. The simple structure of these sys
tems results in interesting geometric properties; one of these is the notion
of spatial equivalence. In this paper, a formal framework for describing
affine hybrid systems is introduced. As an application, it is proven that
every compact hybrid system H is spatially equivalent to a hybrid sys
tem Hid in which all the transition maps are the identity. An explicit
and computable construction for Hid is given.
1 Introduction
This paper introduces affine hybrid systems. Affine hybrid systems are hybrid
systems where the discrete domains are affine sets, and the transition maps be
tween discrete domains are affine transformations. This definition differs from
other definitions of hybrid systems that have been proposed [9], but the under
lying ideas involved in the definition of affine hybrid systems have been seen in
the literature [6,7]. We give a formal framework to these ideas.
