Skip to main content
SpringerLink
Log in

Stabilizability for boundary-value control systems using symbolic calculus of pseudo-differential operators

  • Conference paper
  • First Online:
Nonlinear and Adaptive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 281))

  • 799 Accesses

Abstract

The paper considers control systems which are constructed from certain pseudo-differential and boundary-value operators. The system contains the derivative control which is after a change of variables included in many such situations where the control variables (originally) appear in the boundary condition. Sufficient analytical conditions for some stability properties of the transfer function are shown. In addition, we describe some methods to compute the transfer function by means of symbolic calculus. An illustrative example is considered as well.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • 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.

References

  1. Amann, H. (1989) Feedback stabilization of linear and semilinear parabolic systems. In: Clément et al. (Eds.) Semigroup Theory and Applications, Lecture Notes Pure Appl. Math. 116. M. Dekker, New York, 21–57

    Google Scholar 

  2. Amann, H. (1995) Linear and Quasilinear Parabolic Problems. Vol. I. Abstract Linear Theory. Birkhäuser, Basel

    Google Scholar 

  3. Banks, S.P. (1983) State-space and Frequency-domain Methods in the Control of Distributed Parameter Systems. P. Peregrinus, London

    MATH  Google Scholar 

  4. Callier, F.M., Desoer, C.A. (1982) Multivariable Feedback Systems. Springer, Berlin

    Google Scholar 

  5. Curtain, R.F., Zwart, H.J. (1995) An Introduction to Infinite-Dimensional Linear Systems Theory. Springer, New York

    MATH  Google Scholar 

  6. Fattorini, H.O. (1999) Infinite Dimensional Optimization and Control Theory. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  7. Grubb, G. (1986) Functional Calculus of Pseudo-Differential Boundary Problems. Birkhäuser, Boston

    MATH  Google Scholar 

  8. Grubb, G. (1991) Parabolic Pseudo-Differential Boundary Problems and Applications. In: Cattabriga L., Rodino, L. (Eds.) Microlocal Analysis and Applications, Lecture Notes in Math., Vol. 1495, Springer, Berlin, 46–117

    Chapter  Google Scholar 

  9. Krainer, T. (2000) Parabolic Pseudodifferential Operators and Long-Time Asymptotics of Solutions. PhD Thesis, University of Potsdam, Potsdam

    MATH  Google Scholar 

  10. Mossaheb, S. (1980) On the existence of right-coprime factorization for functions meromorphic in a half-plane. IEEE Trans. Aut. Control AC-25, 550–551

    Article  MathSciNet  Google Scholar 

  11. Pommaret, J.F. (2001) Controllability of nonlinear multidimensional control systems. In: Respondek, W. et al. (Eds.) Nonlinear Control of the Year 2000, Proc. NCN Conference, Vol. 2., Springer, Berlin, 245–255

    Chapter  Google Scholar 

  12. Quadrat, A. (2000) Internal stabilization of coherent control systems. Preprint, 1–16

    Google Scholar 

  13. Rempel, S., Schulze, B.-W. (1982) Index Theory of Elliptic Boundary Problems. Akademie-Verlag, Berlin

    MATH  Google Scholar 

  14. Shulze, B.-W. (1998) Boundary Value Problems and Singular Pseudo-Differential Operators. Wiley

    Google Scholar 

  15. Sule, V.R. (1998) Feedback stabilization over commutative rings: The matrix case. SIAM J. Control and Optimiz. 32, 1675–1695

    Article  MathSciNet  Google Scholar 

  16. Tanabe, H. (1979) Equations of Evolution. Pitman, London

    MATH  Google Scholar 

  17. Tervo, J., Nihtilä, M. (2000) Exponential stability of a nonlinear distributed parameter system. Zeitschrift für Analysis und ihre Anwendungen 19, 77–93

    MATH  Google Scholar 

  18. Vidyasagar, M. (1985) Control System Synthesis. A Factorization Approach. MIT Press, Cambridge

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Applied Mathematics, University of Kuopio, P.O.Box 1627, FIN-70211, Kuopio, Finland

    Markku T. Nihtilä & Jouko Tervo

Authors
  1. Markku T. Nihtilä
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jouko Tervo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departement of AppliedMathematics, The University of Sheffield, Western Bank, Sheffield, S10 2TN, UK

    Alan Zinober

  2. Dept. of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK

    David Owens

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nihtilä, M.T., Tervo, J. (2003). Stabilizability for boundary-value control systems using symbolic calculus of pseudo-differential operators. In: Zinober, A., Owens, D. (eds) Nonlinear and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45802-6_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-45802-6_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43240-1

  • Online ISBN: 978-3-540-45802-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation