Bisimulation equivalence of DAE systems

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.

[1]  G. Basile,et al.  Controlled and conditioned invariants in linear system theory , 1992 .

[2]  George J. Pappas,et al.  Bisimilar control affine systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[3]  S. Campbell.  Singular Systems of Differential Equations , 1980 .

[4]  G. Hayton,et al.  Generalised Autonomous Dynamical Systems, Algebraic Duality and Geometric Theory , 1981 .

[5]  Stephan Trenn,et al.  Solution Concepts for Linear DAEs: A Survey , 2013 .

[6]  V. Armentano.  The pencil (sE-A) and controllability-observability for generalized linear systems: A geometric approach , 1984, The 23rd IEEE Conference on Decision and Control.

[7]  Arjan van der Schaft,et al.  Equivalence of hybrid dynamical systems , 2004 .

[8]  F. Lewis.  A survey of linear singular systems , 1986 .

[9]  P. Bernhard.  On Singular Implicit Linear Dynamical Systems , 1982 .

[10]  T. Berger,et al.  Hamburger Beiträge zur Angewandten Mathematik Controllability of linear differential-algebraic systems-A survey , 2012 .

[11]  A. J. van der Schaft.  Equivalence of dynamical systems by bisimulation , 2004, IEEE Transactions on Automatic Control.

[12]  Arjan van der Schaft,et al.  Equivalence of dynamical systems by bisimulation , 2004, IEEE Trans. Autom. Control..

[13]  George J. Pappas.  Bisimilar linear systems , 2003, Autom..

[14]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[15]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[16]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[17]  Harry L. Trentelman,et al.  Control theory for linear systems , 2002 .