Departmental Papers (ESE)


The notion of exact bisimulation equivalence for nondeterministic discrete systems has recently resulted in notions of exact bisimulation equivalence for continuous and hybrid systems. In this paper, we establish the more robust notion of approximate bisimulation equivalence for nondeterministic nonlinear systems. This is achieved by requiring that a distance between system observations starts and remains, close, in the presence of nondeterministic system evolution. We show that approximate bisimulation relations can be characterized using a class of functions called bisimulation functions. For nondeterministic nonlinear systems, we show that conditions for the existence of bisimulation functions can be expressed in terms of Lyapunov-like inequalities, which for deterministic systems can be computed using recent sum-of-squares techniques. Our framework is illustrated on a safety verification example.

Document Type

Conference Paper

Subject Area


Date of this Version

December 2005


Copyright 2005 IEEE. Reprinted from Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, December 2005, pages 684-689.

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Date Posted: 30 March 2007

This document has been peer reviewed.