Skip to main content
Log in

A Note on the Asymptotic Stability of Fuzzy Differential Equations

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We study the stability of solutions of fuzzy differential equations by Lyapunov's second method. By using scale equations and the comparison principle for Lyapunov-like functions, we give sufficient criteria for the stability and asymptotic stability of solutions of fuzzy differential equations.

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

Access this article

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. D. Driankov, H. Hellendorm, and M. Rein Frank, An Introduction to Fuzzy Control, Springer, Berlin (1996).

    Google Scholar 

  2. D. Dubois and H. Prade, “Towards fuzzy differential calculus. Part I,” Fuzzy Sets Syst., 8, 1–17 (1982).

    MathSciNet  Google Scholar 

  3. D. Dubois and H. Prade, “Towards fuzzy differential calculus. Part II,” Fuzzy Sets Syst., 8, 105–116 (1982).

    MathSciNet  Google Scholar 

  4. D. Dubois and H. Prade, “Towards fuzzy differential calculus. Part III,” Fuzzy Sets Syst., 8, 225–234 (1982).

    MathSciNet  Google Scholar 

  5. O. Kaleva, “On the calculus of fuzzy valued mapping,” Appl. Math. Lett., 3, 55–59 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  6. M. L. Puri and D. A. Ralescu, “Differential of fuzzy functions,” J. Math. Anal. Appl., 91, 552–558 (1983).

    Article  MathSciNet  Google Scholar 

  7. O. Kaleva, “Fuzzy differential equations,” Fuzzy Sets Syst., 24, 301–317 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  8. O. Kaleva, “The Cauchy problem for fuzzy differential equations,” Fuzzy Sets Syst., 35, 389–396 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  9. P. E. Kloeden, “Remark on Peano-like theorems for fuzzy differential equations,” Fuzzy Sets Syst., 44, 161–163 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  10. V. Lakshmikantham and R. N. Mohapatra, “Basic properties of solutions of fuzzy differential equations,” Nonlin. Stud., 8, 113–124 (2000).

    MathSciNet  Google Scholar 

  11. J. J. Nieto, “The Cauchy problem for continuous fuzzy differential equations,” Fuzzy Sets Syst., 102, 259–262 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  12. M. L. Puri and D. A. Ralescu, “Fuzzy random variables,” J. Math. Anal. Appl., 114, 409–422 (1986).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 904–911, July, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Van Hien, L. A Note on the Asymptotic Stability of Fuzzy Differential Equations. Ukr Math J 57, 1066–1076 (2005). https://doi.org/10.1007/s11253-005-0248-x

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-005-0248-x

Keywords

Navigation