Bisimulation equivalence of DAE systems

TL;DR

This paper extends bisimulation concepts to general linear DAE systems, providing a geometric control theory-based algebraic characterization and an algorithm for maximal bisimulation computation, including special cases and simulation notions.

Contribution

It introduces a novel bisimulation framework for linear DAE systems, with algebraic characterizations and algorithms, advancing system equivalence analysis.

Findings

Derived a linear-algebraic characterization of bisimulation relations.

Developed an algorithm to compute the maximal bisimulation relation.

Extended the framework to regular matrix pencil cases and simulation concepts.

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.