Departmental Papers (ESE)


The notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation. These equivalences are in turn used to simplify verification and synthesis for these models as well as to enable compositional reasoning. In systems theory, a similar notion is also of interest in order to develop modular verification and design tools for purely continuous or hybrid control systems. In this paper, we introduce two notions of bisimulation for nonlinear systems. We present differential-algebraic characterizations of these notions and show that bisimilar systems of different dimensions are obtained by factoring out certain invariant distributions. Furthermore, we also show that all bisimilar systems of different dimension are of this form.

Document Type

Journal Article

Subject Area


Date of this Version

May 2004


Postprint version. Published in Systems and Control Letters, Volume 52, Issue 1, May 2004, pages 49-58.
Publisher URL:


bisimulation relations, bisimilar control systems, controlled invariance, symmetries



Date Posted: 15 March 2006

This document has been peer reviewed.