Asymptotic estimates and exponential stability for higher-order monotone difference equations
Advances in Difference Equations volume 2005, Article number: 947201 (2005)
Asymptotic estimates are established for higher-order scalar difference equations and inequalities the right-hand sides of which generate a monotone system with respect to the discrete exponential ordering. It is shown that in some cases the exponential estimates can be replaced with a more precise limit relation. As corollaries, a generalization of discrete Halanay-type inequalities and explicit sufficient conditions for the global exponential stability of the zero solution are given.
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Liz, E., Pituk, M. Asymptotic estimates and exponential stability for higher-order monotone difference equations. Adv Differ Equ 2005, 947201 (2005). https://doi.org/10.1155/ADE.2005.41