Bisimulation equivalence of DAE systems

Abstract

In this paper the notion of bisimulation relation for linear input-state-output systems is extended to general linear differential-algebraic (DAE) systems. Geometric control theory is used to derive a linear-algebraic characterization of bisimulation relations, and an algorithm for computing the maximal bisimulation relation between two linear DAE systems. The general definition is specialized to the case where the matrix pencil \(sE - A\) is regular. Furthermore, by developing a one-sided version of bisimulation, characterizations of simulation and abstraction are obtained. Moreover, it is shown how state space reduction is performed by computing the maximal bisimulation relation between the DAE system and itself.