GENERALIZED DISCRETE HALANAY INEQUALITIES AND THE ASYMPTOTIC BEHAVIOR OF NONLINEAR DISCRETE SYSTEMS Xu, Liguang;
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].
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
2.
Exponential ultimate boundedness of nonlinear stochastic difference systems with time-varying delays, International Journal of Control, 2015, 1
3.
Stability analysis of a general family of nonlinear positive discrete time-delay systems, International Journal of Control, 2016, 89, 7, 1303
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