A comment on “Exponential stability of nonlinear delay equation with constant decay rate via perturbed system method”

International Journal of Control, Automation and Systems

Volumn 12, Issue 6, 2014, Pages 1352-1357

  Makhlouf, Abdellatif Ben ^a   Hammami, Mohamed Ali ^a  

^a UNIVERSITY OF SFAX   (Tunisia)

Author keywords

Exponential stability; nonlinear inequality; time delay; time varying systems

Indexed keywords

ASYMPTOTIC STABILITY; DECAY (ORGANIC); NONLINEAR EQUATIONS; TIME DELAY; TIME VARYING SYSTEMS;

DECAY RATE; DELAY EQUATIONS; NONLINEAR INEQUALITY; PERTURBED SYSTEMS;

SYSTEM STABILITY;

EID: 84919460870     PISSN: 15986446     EISSN: 20054092     Source Type: Journal    
DOI: 10.1007/s12555-014-0015-6     Document Type: Article

References (11)

1. D. Bainov and P. Simeonov, Integral Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 1992.
2. R. Bellman, “The stability of solutions of linear differential equations,” Duke Math. J., vol. 10, pp. 643–647, 1943.
3. S. S. Dragomir, “Some Gronwall type inequalities and applications,” RGMIA Monographs, Victoria University, Australia, 2000.
4. 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.
5. 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.
6. X. Mao, “Exponential stability of nonlinear differential delay equations,” Systems Control Letters, vol. 28, no. 3, pp. 159–165, 1996.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.