A new result on the global exponential stability of nonlinear neutral volterra integro-differential equation with variable lags

Volume 5, Issue 1, pp 29--43 http://dx.doi.org/10.22436/mns.05.01.04

Publication Date: April 06, 2020 Submission Date: February 18, 2018 Revision Date: December 02, 2019 Accteptance Date: December 06, 2019

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1507 Downloads
• 2076 Views

Authors

Yener Altun - Ercis Management Faculty, Department of Business Administration, Yuzuncu Yil University, 65080, Van, Turkey.

Abstract

In this study, the global exponential stability (GES) of the zero solution of a nonlinear neutral volterra integro-differential equation (NVIDE) with variable lags has been investigated. Based on the Lyapunov functional approach, a new stability criterion was derived for global exponential stability criterions of the considered equation. An example with numeric simulation has been given to demonstrate the applicability and accuracy of the obtained result by MATLAB Simulink.

Share and Cite

Keywords

• NVIDE
• GES
• Lyapunov functional
• variable lags

MSC

•  34K20
•  34K40

References

• [1] R. P. Agarwal, S. R. Grace, Asymptotic stability of certain neutral differential equations, Math. Comput. Modelling, 31 (2000), 9--15
  • Google Scholar


• [2] Y. Altun, C. Tunc, On the global stability of a neutral differential equation with variable time-lags, Bull. Math. Anal. Appl., 9 (2017), 31--41
  • Google Scholar


• [3] D. Arslan, A novel hybrid method for singularly perturbed delay differential equations, Gazi University Journal of Science, 32 (2019), 217--223
  • Google Scholar


• [4] M. Cakir, D. Arslan, The Adomian decomposition method and the differential transform method for numerical solution of multi-pantograph delay differential equations, Applied Mathematics, 6 (2015), 1332--1343
  • Google Scholar


• [5] H. Chen, Some improved criteria on exponential stability of neutral differential equation, Adv. Difference Equ., 2012 (2012), 9 pages
  • Google Scholar


• [6] H. Chen, X. Meng, An improved exponential stability criterion for a class of neutral delayed differential equations, Appl. Math. Lett., 24 (2011), 1763--1767
  • Google Scholar


• [7] S. Deng, X. Liao, S. Guo, Asymptotic stability analysis of certain neutral differential equations: a descriptor system approach, Math. Comput. Simulation, 79 (2009), 2981--2993
  • Google Scholar


• [8] H. A. El-Morshedy, K. Gopalsamy, Nonoscillation, oscillation and convergence of a class of neutral equations, Nonlinear Anal., 40 (2000), 173--183
  • Google Scholar


• [9] E. Fridman, Stability of linear descriptor systems with delays a Lyapunov-based approach, J. Math. Anal. Appl., 273 (2002), 24--44
  • Google Scholar


• [10] J. K. Hale, S. M. V. Lunel, Introduction to functional-differential equations, Springer-Verlag, New York (1993)
  • Google Scholar


• [11] P. Keadnarmol, T. Rojsiraphisal, Globally exponential stability of a certain neutral differential equation with time-varying delays, Adv. Difference Equ., 2014 (2014), 10 pages
  • Google Scholar


• [12] O. M. Kwon, J. H. Park, On improved delay-dependent stability criterion of certain neutral differential equations, Appl. Math. Comput., 199 (2008), 385--391
  • Google Scholar


• [13] O. M. Kwon, J. H. Park, S. M. Lee, Augmented Lyapunov functional approach to stability of uncertain neutral systems with time-varying delays, Appl. Math. Comput., 207 (2009), 202--212
  • Google Scholar


• [14] X. Li, Global exponential stability for a class of neural networks, Appl. Math. Lett., 22 (2009), 1235--1239
  • Google Scholar


• [15] X. Liao, Y. Liu, S. Guo, H. Mai, Asymptotic stability of delayed neural networks: a descriptor system approach, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 3120--3133
  • Google Scholar


• [16] P. T. Nam, V. N. Phat, An improved stability criterion for a class of neutral differential equations, Appl. Math. Lett., 22 (2009), 31--35
  • Google Scholar


• [17] J. H. Park, Delay-dependent criterion for asymptotic stability of a class of neutral equations, Appl. Math. Lett., 17 (2004), 1203--1206
  • Google Scholar


• [18] J. H. Park, O. M. Kwon, Stability analysis of certain nonlinear differential equation, Chaos Solitons Fractals, 37 (2008), 450--453
  • Google Scholar


• [19] T. Rojsiraphisal, P. Niamsup, Exponential stability of certain neutral differential equations, Appl. Math. Comput., 217 (2010), 3875--3880
  • Google Scholar


• [20] Y. G. Sun, L. Wang, Note on asymptotic stability of a class of neutral differential equations, Appl. Math. Lett., 19 (2006), 949--953
  • Google Scholar


• [21] C. Tunc, Convergence of solutions of nonlinear neutral differential equations with multiple delays, Bol. Soc. Mat. Mex., 21 (2015), 219--231
  • Google Scholar


• [22] C. Tunc¸, Y. Altun, Asymptotic stability in neutral differential equations with multiple delays, J. Math. Anal., 7 (2016), 40--53
  • Google Scholar


• [23] C. Tunc¸, Y. Altun, On the nature of solutions of neutral differential equations with periodic coefficients, Appl. Math. Inf. Sci. (AMIS), 11 (2017), 393--399
  • Google Scholar