JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GENERALIZED DISCRETE HALANAY INEQUALITIES AND THE ASYMPTOTIC BEHAVIOR OF NONLINEAR DISCRETE SYSTEMS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
GENERALIZED DISCRETE HALANAY INEQUALITIES AND THE ASYMPTOTIC BEHAVIOR OF NONLINEAR DISCRETE SYSTEMS
Xu, Liguang;
  PDF(new window)
 Abstract
In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90] and [S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859].
 Keywords
Halanay inequality;discrete systems;attracting set;global asymptotic stability;
 Language
English
 Cited by
1.
Multi-dimensional discrete Halanay inequalities and the global stability of the disease free equilibrium of a discrete delayed malaria model, Advances in Difference Equations, 2016, 2016, 1  crossref(new windwow)
2.
Exponential ultimate boundedness of nonlinear stochastic difference systems with time-varying delays, International Journal of Control, 2015, 1  crossref(new windwow)
3.
Stability analysis of a general family of nonlinear positive discrete time-delay systems, International Journal of Control, 2016, 89, 7, 1303  crossref(new windwow)
 References
1.
R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90.

2.
R. P. Agarwal and P. J. Y. Wong, Advanced Topics in Difference Equations, in: Math-ematics and its Applications, vol. 404, Kluwer, Dordrecht, 1997.

3.
C. T. H. Baker, Development and application of Halanay-type theory: Evolutionary differential and difference equations with time lag, J. Comput. Appl. Math. 234 (2010), no. 9, 2663-2682. crossref(new window)

4.
E. Beckenbach and R. Bellman, Inequalities, Springer-Verlag, New York, 1961.

5.
L. Berezansky, L. Idels, and L. Troib, Global dynamics of one class of nonlinear nonau-tonomous systems with time-varying delays, Nonlinear Anal. 74 (2011), no. 18, 7499-7512. crossref(new window)

6.
J. D. Cao and J. Wang, Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays, Neural Networks 17 (2004), 379-390. crossref(new window)

7.
E. Fridman and A. Blighovsky, Robust sampled-data control of a class of semilinear parabolic systems, Automatica J. IFAC 48 (2012), no. 5, 826-836. crossref(new window)

8.
K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic, Dordrecht, 1992.

9.
A. Halanay, Differential Equations: Stability, Oscillations, Time Lags, Academic Press, New York, 1966.

10.
E. Liz and J. B. Ferreiro, A Note on the global stability of generalized difference equations, Appl. Math. Lett. 15 (2002), no. 6, 655-659. crossref(new window)

11.
E. Liz and S. Trofimchuk, Existence and stability of almost periodic solutions for quasilinear delay systems and Halanay inequality, J. Math. Anal. Appl. 248 (2000), no. 2, 625-644. crossref(new window)

12.
S. Mohamad, Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks, Phys. D 159 (2001), no. 3-4, 233-251 crossref(new window)

13.
S. Mohamad, K. Gopalsamy, and H. Akca, Exponential stability of artificial neural networks with distributed delays and large impulses, Nonlinear Anal. Real World Appl. 9 (2008), no. 3, 872-888. crossref(new window)

14.
P. Niamsup, Stability of time-varying switched systems with time-varying delay, Non-linear Anal. Hybrid Syst. 3 (2009), no. 4, 631-639. crossref(new window)

15.
H. J. Tian, The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag, J. Math. Anal. Appl. 270 (2002), no. 1, 143-149. crossref(new window)

16.
S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859. crossref(new window)

17.
L. P. Wen, Y. X. Yu, and W. S. Wang, Generalized Halanay inequalities for dissipativity of Volterra functional differential equations, J. Math. Anal. Appl. 347 (2008), no. 1, 169-178. crossref(new window)

18.
D. Y. Xu and X. H. Wang, A new nonlinear integro-differential inequality and its application, Appl. Math. Lett. 22 (2009), no. 11, 1721-1726. crossref(new window)

19.
D. Y. Xu and L. G. Xu, New results for studying a certain class of nonlinear delay differential systems, IEEE Trans. Automat. Control 55 (2010), no. 7, 1641-1645. crossref(new window)

20.
D. Y. Xu and Z. C. Yang, Impulsive delay differential inequality and stability of neural networks, J. Math. Anal. Appl. 305 (2005), no. 1, 107-120. crossref(new window)

21.
L. G. Xu, Exponential P-stability of singularly perturbed impulsive stochastic delay differential systems, Int. J. Control, Autom. 9 (2011), 966-972. crossref(new window)

22.
L. G. Xu and D. H. He, Mean square exponential stability analysis of impulsive stochastic switched systems with mixed delays, Comput. Math. Appl. 62 (2011), no. 1, 109-117. crossref(new window)

23.
L. G. Xu and D. Y. Xu, Exponential stability of nonlinear impulsive neutral integro-differential equations, Nonlinear Anal. 69 (2008), no. 9, 2910-2923. crossref(new window)

24.
Z. G. Yang and D. Y. Xu, Mean square exponential stability of impulsive stochastic difference equations, Appl. Math. Lett. 20 (2007), no. 8, 938-945. crossref(new window)

25.
H. Y. Zhao, L. Sun, and G. L. Wang, Periodic oscillation of discrete-time bidirectional associative memory neural networks, Neurocomputing 70 (2007), 2924-2930. crossref(new window)