1887
Volume 2014, Issue 1
  • EISSN: 2223-506X

Abstract

We consider the vibrations of electrical waves or telecommunication signals. The uniform stabilization of such vibrations is directly established with an explicit form of exponential energy decay estimate. Using the fuzzy transform method, a closed form numerical scheme is constructed to support the stability result.

Loading

Article metrics loading...

/content/journals/10.5339/connect.2014.19
2014-09-01
2024-11-07
Loading full text...

Full text loading...

/deliver/fulltext/connect/2014/1/connect.2014.19.html?itemId=/content/journals/10.5339/connect.2014.19&mimeType=html&fmt=ahah

References

  1. Hodgkin AL, Huxley AF. A quantitative description of membrane current and it's application to coduction and excitation in nerve. J Physiol. 1952; 117::500544.
    [Google Scholar]
  2. Chen G. Energy decay estimates and exact boundary-value controllability for the wave equation in a bounded domain. J Math Pures Appl. 1979; 58::249273.
    [Google Scholar]
  3. Chen G. A note on the boundary stabilization of the wave equation. SIAM J Control Optim. 1981; 19:1:106113.
    [Google Scholar]
  4. Gorain GC. Exponential energy decay estimate for the solutions of internally damped wave equation in a bounded domain. J Math Anal Appl. 1997; 216:2:510520.
    [Google Scholar]
  5. Gorain GC. Exponentially energy decay estimate for the solutions of n- dimensional Kirchhoff type wave equation. Appl Math Comput. 2006; 177:1:235242.
    [Google Scholar]
  6. Komornik V, Zuazua E. A direct method for the boundary stabilization of the wave equation. J Math Pures Appl. 1990; 69:1:3354.
    [Google Scholar]
  7. Saharuz SM. Bounded-Input-Bounded-Output stability of damped non-linear string. IEEE Trans Automat Control. 1996; 41:8:11791182.
    [Google Scholar]
  8. Nandi PK, Gorain GC, Kar S. Boundary stabilization of torsional vibration of a solar panel. Appl Appl Math. 2012; 7:1:455463.
    [Google Scholar]
  9. Gorain GC. Stabilization of a quasi-linear vibrations of an inhomogeneous beam. IEEE Trans Automat Control. 2007; 52:9:16901695.
    [Google Scholar]
  10. Lagnese J. Note on boundary stabilization of wave equation. SIAM J Control Optim. 1988; 26::12501256.
    [Google Scholar]
  11. Nandi PK, Gorain GC, Kar S. Uniform exponential stabilization for flexural vibrations of a solar panel. Appl Math. 2011; 2:6:661665.
    [Google Scholar]
  12. Stepnicka M. Fuzzy transformation and its application in A/D Converter. J Electr Eng. 2003; 54:12:7275.
    [Google Scholar]
  13. Perfilieva I, Chaldeeva E. Fuzzy transformation and its applications. In the Proceedings of the 4th Czech – Japan seminar on data analysis and decision making under uncertainty, 2001;:116124.
  14. Zadeh LA. Fuzzy sets and systems, system theory. Int J Gen Syst. 1990; 17::129138.
    [Google Scholar]
  15. Mitrinovic DS, Pecaric JE, Fink AM. Inequalities involving functions and their integrals and derivatives. Dordrecht, Netherlands: Kluwer 1991.
    [Google Scholar]
  16. Komornik V. Exact controllability and stabilization. The Multiplier Method. Paris: Wiley-Masson 1994.
    [Google Scholar]
  17. Fung YC. Foundations of solid mechanics. New Delhi: Prentice-Hall 1968.
    [Google Scholar]
/content/journals/10.5339/connect.2014.19
Loading
/content/journals/10.5339/connect.2014.19
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error