System Theoretic Foundations for Modelling Physical Systems

  • Jan C. Willems
Part of the International Centre for Mechanical Sciences book series (CISM, volume 261)


In this paper we will outline the main ideas of an axiomatic approach to the modelling of dynamical systems. This approach differs from the usual one in that the input/output, i.e., the cause/effect relationship is not assumed to be given a priori. More details on the theoretical developments and examples from physics may be found in [1]. These ideas are here applied to time-reversibility, where it is shown how one may deduce the existence of a time-reversing involution on the state space.


State Space Axiomatic Approach State Space Form External Behavior Minimal Realization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J.C. Willems, “System Theoretic Models for the Analysis of Physical Systems”, to appear in Ricerche di Automatica, 1980.Google Scholar
  2. [2]
    R.E. Kalman, P.L. Falb, and M. Arbib, Topics in Mathematical System Theory, McGraw-Hill, 1969.Google Scholar
  3. [3]
    J.C. Willems, “Time Reversibility in Deterministic and Stochastic Dynamical Systems”, pp. 318–326 of Recent Developments in Variable Structure Systems, Economics and Biology (Eds.: R.R. Mohler and A. Ruberti), Vol. 162 of Springer Lecture Notes in Economics and Mathematical Systems, 1978.Google Scholar

Copyright information

© Springer-Verlag Wien 1980

Authors and Affiliations

  • Jan C. Willems
    • 1
  1. 1.Mathematics InstituteGroningenThe Netherlands

Personalised recommendations