Departmental Papers (ESE)


In this paper, we define the notion of approximate bisimulation relation between two continuous systems. While exact bisimulation requires that the observations of two systems are and remain identical, approximate bisimulation allows the observations to be different provided the distance between them remains bounded by some parameter called precision. Approximate bisimulation relations are conveniently defined as level sets of a so-called bisimulation function which can be characterized using Lyapunov-like differential inequalities. For a class of constrained linear systems, we develop computationally effective characterizations of bisimulation functions that can be interpreted in terms of linear matrix inequalities and optimal values of static games. We derive a method to evaluate the precision of the approximate bisimulation relation between a constrained linear system and its projection. This method has been implemented in a Matlab toolbox: MATISSE. An example of use of the toolbox in the context of safety verification is shown.

Document Type

Journal Article

Subject Area


Date of this Version

August 2007


Postprint version. Published in Automatica, Volume 43, Issue 8, August 2007, 1307-1317.
Publisher URL:


abstractions, approximation, bisimulation, lyapunov techniques, safety



Date Posted: 26 October 2007

This document has been peer reviewed.