Departmental Papers (CIS)

Document Type

Journal Article

Date of this Version

July 2000

Publication Title

Proceedings of the IEEE

Volume

88

Issue

7

First Page

971

Last Page

984

DOI

10.1109/5.871304

Abstract

A hybrid system is a dynamical system with both discrete and continuous state changes. For analysis purposes, it is often useful to abstract a system in a way that preserves the properties being analyzed while hiding the details that are of no interest. We show that interesting classes of hybrid systems can be abstracted to purely discrete systems while preserving all properties that are definable in temporal logic. The classes that permit discrete abstractions fall into two categories. Either the continuous dynamics must be restricted, as is the case for timed and rectangular hybrid systems, or the discrete dynamics must be restricted, as is the case for o-minimal hybrid systems. In this paper, we survey and unify results from both areas.

Permission Statement

© 2000 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Keywords

abstraction, decidability, hybrid systems, logic, model checking, discrete systems, temporal logic, continuous dynamics, discrete abstractions, discrete systems, o-minimal hybrid systems, rectangular hybrid systems, temporal logic, timed hybrid systems

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Date Posted: 30 April 2005

This document has been peer reviewed.