Departmental Papers (ESE)


The fundamental notion of bisimulation equivalence for concurrent processes, has escaped the world of continuous, and subsequently, hybrid systems. Inspired by the categorical framework of Joyal, Nielsen and Winskel, we develop novel notions of bisimulation equivalence for dynamical systems as well as control systems. We prove that this notion can be captured by the abstract notion of bisimulation as developed by Joyal, Nielsen and Winskel. This is the first unified notion of system equivalence that transcends discrete and continuous systems. Furthermore, this enables the development of a novel and natural notion of bisimulation for hybrid systems, which is the final goal of this paper. This completes our program of unifying bisimulation notions for discrete, continuous and hybrid systems.

Document Type

Journal Article

Subject Area


Date of this Version

September 2005


Postprint version. Published in Theoretical Computer Science, Volume 342, Issues 2-3, September 7, 2005, pages 229-261.
Publisher URL:


Bisimulation, open maps, dynamical systems, control systems, hybrid systems



Date Posted: 14 April 2006

This document has been peer reviewed.