Skip to main content
SpringerLink
Log in

On evolution of open dynamical systems: Some algebraic methods

  • Published:
Open Systems & Information Dynamics

Abstract

Open dynamical systems which are governed by a finite number of ordinary differential equations with controls (time-dependent control parameters) constitute a large and important class of models for practical purposes. In the last few years, there has been considerable interest and progress in algebraic methods for solving the equations of the form

$$\dot x\left( t \right) = L_0 x\left( t \right) + \sum\limits_{j = 1}^r {u\left( t \right)L_i x\left( t \right)} ,$$
((*))

i.e. bilinear models. In this paper, intended as an expository introduction to the main results of system-theoretic approach to the modelling of open systems, a new “polynomial” representation of solutions to (*) is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. J. van der Schaft,System Theoretic Description of Physical Systems, CWI Tract 3, Amsterdam, 1984.

    Google Scholar 

  2. A. Tannenbaum,Invariance and System Theory: Algebraic and Geometric aspects, LNM 845, Springer-Verlag, Berlin, 1981.

    Google Scholar 

  3. C. A. Mead, Rev. Mod. Phys.64, 51 (1992).

    Google Scholar 

  4. N. Goel, S. Maitra and E. Montroll, Rev. Mod. Phys.43, 231 (1971).

    Google Scholar 

  5. J. Wei and E. Norman, J. Math. Phys.4, 575 (1963).

    Google Scholar 

  6. J. Wei and E. Norman, Proc. Am. Math. Soc.15, 327 (1964).

    Google Scholar 

  7. G. Dattoli, A. Torre, and J. C. Gallardo, Riv. Nuovo Cimento11, 1 (1988).

    Google Scholar 

  8. J. N. Elgin, Phys. Lett. A80, 140 (1980).

    Google Scholar 

  9. F. T. Hioe and J. H. Eberly, Phys. Rev. Lett.47, 838 (1981).

    Google Scholar 

  10. F. T. Hioe, inLasers, Molecules, and Methods, ed. by J. O. Hirschfelder, J. Wiley, New York, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Physics, Nicholas Copernicus University, Toruń, Poland

    A. Jamiolkowski

  2. Fachbereich Physik, Carl von Ossietzky Universität, Oldenburg, Germany

    K. Haubold

Authors
  1. A. Jamiolkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Haubold
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jamiolkowski, A., Haubold, K. On evolution of open dynamical systems: Some algebraic methods. Open Syst Inf Dyn 1, 291–302 (1992). https://doi.org/10.1007/BF02228950

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02228950

Keywords

Search

Navigation