Skip to main content

Realization Theory of Bilinear Systems

  • Conference paper
Geometric Methods in System Theory

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 3))

Abstract

Interest in bilinear systems theory and applications has grown in the recent years. The basic motivation of this growth is twofold: on the one hand, the feasibility to be a satisfactory model for large classes of systems (physical, biological, socio-economical, etc.); on the other hand the relative ease with which their theory can be set-up. The first characteristic is substantially related to the presence of a multiplicative control action (on the state motion) besides the additive one, which is the only one present in a linear system. The second characteristic lies in the fact that, for any fixed input, the equations are linear in the state.

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

Access this chapter

Subscribe and save

Springer+ Basic
€32.70 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (France)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 42.79
Price includes VAT (France)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 52.74
Price includes VAT (France)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. R.R.MOHLER, Bilinear control processes with applications to engineering, ecology and medicine, Academic Press, New York (1973).

    MATH  Google Scholar 

  2. C.BRUNI, G.DI PILLO, G.KOCH, Bilinear systems: an appealing class of “nearly linear” systems in theory and applications. IEEE Trans. Automatic Control, AC 19 (1974), to appear.

    Google Scholar 

  3. P.d’ALESSANDRO, A.ISIDORI, R.RUBERTI, Realization and structure theory of bilinear dynamical systems, SIAM J. Control, 12 (1974), to appear.

    Google Scholar 

  4. P.d’ALESSANDRO, A.ISIDORI, R.RUBERTI, Lectures an Bilinear System Theory, Notes for a Course held at C.I.S.M., Udine (Italy), Springer Verlag (Wien), 1972.

    Google Scholar 

  5. R.W.BROCKETT, On the algebraic structure of bilinear systems, Theory and Applications of Variable Structure Systems (R.R. Mohler and A. Ruberti, eds.), Academic Press, New York (1972), pp. 153–168.

    Google Scholar 

  6. A.ISIDORI, Direct construction of minimal bilinear realizations from nonlinear input/output maps, IEEE Trans. Automatic Control, AC 18 (1973), to appear.

    Google Scholar 

  7. A.ISIDORI, The computation of reduced forms for bilinear systems, Ricerche di Automatica, 3 (1972), pp. 296–299.

    Google Scholar 

  8. C.BRUNI, G.DI PILLO, G.KOCH, On the mathematical models of bilinear systems, Ricerche di Automatica, 2 (1971), pp. 11–26.

    Google Scholar 

  9. R.E.KALMAN, P.L.FALB, M.A.ARBIB, Topics in mathematical system Theory, Mc Graw Hill (New York), 1969, pp. 288–308.

    Google Scholar 

  10. A.J.TETHER, Construction of linear state-variable models from finite input/output data, IEEE Trans. Automatic Control, AC 15 (1970), pp. 427–436.

    Article  MathSciNet  Google Scholar 

  11. H.H.ROSENBROCK, Computation of minimal representation of rational transfer function matrix, Proc. IEE, 115 (1968), pp. 325–7.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

D. Q. Mayne R. W. Brockett

Rights and permissions

Reprints and permissions

Copyright information

© 1973 D. Reidel Publishing Company, Dordrecht

About this paper

Cite this paper

Isidori, A., Ruberti, A. (1973). Realization Theory of Bilinear Systems. In: Mayne, D.Q., Brockett, R.W. (eds) Geometric Methods in System Theory. NATO Advanced Study Institutes Series, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2675-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-2675-8_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-2677-2

  • Online ISBN: 978-94-010-2675-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics