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Affine Hybrid Systems Aaron D. Ames and Shankar Sastry
 

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.

  

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

 

Collections: Engineering