Nasze serwisy używają informacji zapisanych w plikach cookies. Korzystając z serwisu wyrażasz zgodę na używanie plików cookies zgodnie z aktualnymi ustawieniami przeglądarki, które możesz zmienić w dowolnej chwili. Więcej informacji odnośnie plików cookies.

Obowiązek informacyjny wynikający z Ustawy z dnia 16 listopada 2012 r. o zmianie ustawy – Prawo telekomunikacyjne oraz niektórych innych ustaw.

Wyłącz komunikat

 
 

Logowanie

Logowanie za pomocą Centralnej Usługi Uwierzytelniania PRz. Po zakończeniu pracy nie zapomnij zamknąć przeglądarki.

Journal of Mathematics and Applications

Journal of Mathematics and Applications
08/41, DOI: 10.7862/rf.2018.8

On the Exponential Stability of a Neutral Differential Equation of First Order

Melek Gözen, Cemil Tunç

DOI: 10.7862/rf.2018.8

Abstract

In this work, we establish some assumptions that guaranteeing the global exponential stability (GES) of the zero solution of a neutral differential equation (NDE). We aim to extend and improves some results found in the literature.

Full text (pdf)

References

  1. [1] R.P. Agarwal, S.R. Grace, Asymptotic stability of certain neutral differential equations, Math. Comput. Modelling 31 (8-9) (2000) 9-15.
  2. H. Chen, X. Meng, An improved exponential stability criterion for a class of neutral delayed differential equations, Appl. Math. Lett. 24 (11) (2011) 1763-1767.
  3. H. Chen, Some improved criteria on exponential stability of neutral differential equation, Adv. Difference Equ. 2012 (2012:170) 9 pp.
  4. S. Deng, X. Liao, S. Guo, Asymptotic stability analysis of certain neutral differential equations: a descriptor system approach, Math. Comput. Simulation 79 (10) (2009) 2981-2993.
  5. H.A. El-Morshedy, K. Gopalsamy, Non-oscillation, oscillation and convergence of a class of neutral equations. Lakshmikantham's legacy: a tribute on his 75th birthday, Nonlinear Anal. 40 (1-8) (2000) Ser. A: Theory Methods 173-183.
  6. E. Fridman, New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems, Systems Control Lett. 43 (4) (2001) 309-319.
  7. M.R.S. Kulenovic, G. Ladas, A. Meimaridou, Necessary and sufficient condition for oscillations of neutral differential equations, J. Austral. Math. Soc. Ser. B 28 (3) (1987) 362-375.
  8. O.M. Kwon, Ju H. Park, On improved delay-dependent stability criterion of certain neutral differential equations, Appl. Math. Comput. 199 (1) (2008) 385-391.
  9. X. Li, Global exponential stability for a class of neural networks, Appl. Math. Lett. 22 (8) (2009) 1235-1239.
  10. P.T. Nam, V.N. Phat, An improved stability criterion for a class of neutral differential equations, Appl. Math. Lett. 22 (1) (2009) 31-35.
  11. Ju H. Park, S. Won, Stability analysis for neutral delay-differential systems, J. Franklin Inst. 337 (1) (2000) 1-9.
  12. Ju H. Park, Ho Y. Jung, On the exponential stability of a class of nonlinear systems including delayed perturbations, J. Comput. Appl. Math. 159 (2) (2003) 467-471.
  13. J.H. Park, Delay-dependent criterion for asymptotic stability of a class of neutral equations, Appl. Math. Lett. 17 (10) (2004) 1203-1206.
  14. Ju H. Park, O. Kwon, On new stability criterion for delay-differential systems of neutral type, Appl. Math. Comput. 162 (2) (2005) 627-637.
  15. Ju H. Park, O.M. Kwon, Stability analysis of certain nonlinear differential equation, Chaos Solitons Fractals 37 (2) (2008) 450-453.
  16. T. Rojsiraphisal, P. Niamsup, Exponential stability of certain neutral differential equations, Appl. Math. Comput. 217 (8) (2010) 3875-3880.
  17. Y.G. Sun, L. Wang, Note on asymptotic stability of a class of neutral differential equations, Appl. Math. Lett. 19 (9) (2006) 949-953.
  18. C. Tunç, Asymptotic stability of nonlinear neutral differential equations with constant delays: a descriptor system approach, Ann. Differential Equations 27 (1) (2011) 1-8.
  19. C. Tunç, Exponential stability to a neutral differential equation of first order with delay, Ann. Differential Equations 29 (3) (2013) 253-256.
  20. C. Tunç, Asymptotic stability of solutions of a class of neutral differential equations with multiple deviating arguments, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 57 (105) (1) (2014) 121-130.
  21. C. Tunç, On the uniform asymptotic stability to certain first order neutral differential equations, Cubo 16 (2) (2014) 111-119.
  22. C. Tunç, Convergence of solutions of nonlinear neutral differential equations with multiple delays, Bol. Soc. Mat. Mex. 21 (2) (2015) 219-231.
  23. C. Tunç, Y. Altun, Asymptotic stability in neutral differential equations with multiple delays, J. Math. Anal. 7 (5) (2016) 40-53.
  24. C. Tunç, A. Sirma, Stability analysis of a class of generalized neutral equations, J. Comput. Anal. Appl. 12 (4) (2010) 754-759.
  25. S. Xu, J. Lam, Improved delay-dependent stability criteria for time-delay systems, IEEE Trans. Automat. Control 50 (3) (2005) 384-387.

About this Article

TITLE:
On the Exponential Stability of a Neutral Differential Equation of First Order

AUTHORS:
Melek Gözen (1)
Cemil Tunç (2)

AUTHORS AFFILIATIONS:
(1) Department of Business Administration, Management Faculty, Van Yuzuncu Yil University, TURKEY
(2) Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yıl University, TURKEY

JOURNAL:
Journal of Mathematics and Applications
08/41

KEY WORDS AND PHRASES:
(GES); (NDE); Time-varying delays

FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/71

DOI:
10.7862/rf.2018.8

URL:
http://dx.doi.org/10.7862/rf.2018.8

RECEIVED:
2017-09-07

COPYRIGHT:
Publishing House of Rzeszow University of Technology Powstańców Warszawy 12, 35-959 Rzeszow

POLITECHNIKA RZESZOWSKA im. Ignacego Łukasiewicza; al. Powstańców Warszawy 12, 35-959 Rzeszów
tel.: +48 17 865 11 00, fax.: +48 17 854 12 60
Administrator serwisu: