Abstract
In this paper, we point out that inequality (7) of [5] is not correct. A feasible modified and corrected version of the main result is presented. Furthermore, some numerical examples are given to illustrate the applicability of the modified result.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Bainov and P. Simeonov, Integral Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 1992.
R. Bellman, “The stability of solutions of linear differential equations,” Duke Math. J., vol. 10, pp. 643–647, 1943.
S. S. Dragomir, “Some Gronwall type inequalities and applications,” RGMIA Monographs, Victoria University, Australia, 2000.
T. H. Gronwall, “Note on the derivatives with respect to a parameter of the solutions of a system of differential equations,” Ann. Math., vol. 20, pp. 293–296, 1919.
H. Wang, C. Li, and H. Xu, “Exponential stability of nonlinear delay equation with constant decay rate via perturbed system method,” International Journal of Control, Automation and Systems, vol. 8, no. 5, pp. 1148–1152, 2010.
X. Mao, “Exponential stability of nonlinear differential delay equations,” Systems Control Letters, vol. 28, no. 3, pp. 159–165, 1996.
C. Li and Y. Qiu, “Comments on Exponential stability of nonlinear differential delay equations,” Systems Control Letters, vol. 57, no. 10, pp. 834–835, 2008.
V. Singh, “Some remarks on global asymptotic stability of neural networks with constant time delay,” Chaos, Solitons and Fractals, vol. 32, no. 5, pp. 1720–1724, 2007.
S. Arik, “Global asymptotic stability of a larger class of neural networks with constant time delays,” Phys. Lett., vol. 311, no. 6, pp. 504–511, 2003.
V. Singh, “A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks,” IEEE Trans. Neural Network, vol. 15, no. 1, pp. 223–225, 2004.
A. Chen, J. Cao, and L. Huang, “An estimation of upperbound of delays for global asymptotic stability of delayed Hopfield neural networks,” IEEE Trans. Circuits Syst I, vol. 49, no. 7, pp. 1028–1032, 2002.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Editor Ju Hyun Park.
The authors wish to thank the reviewers for their valuable and careful comments.
Rights and permissions
About this article
Cite this article
Makhlouf, A.B., Hammami, M.A. A comment on “Exponential stability of nonlinear delay equation with constant decay rate via perturbed system method”. Int. J. Control Autom. Syst. 12, 1352–1357 (2014). https://doi.org/10.1007/s12555-014-0015-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-014-0015-6