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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 3760262, 8 pages
http://dx.doi.org/10.1155/2016/3760262
Research Article

The Equivalence of Datko and Lyapunov Properties for ()-Trichotomic Linear Discrete-Time Systems

1Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, Vasile Pârvan Boulevard No. 4, 300223 Timişoara, Romania
2Academy of Romanian Scientists, Independenţei 54, 050094 Bucharest, Romania

Received 22 July 2015; Accepted 26 January 2016

Academic Editor: Allan C. Peterson

Copyright © 2016 Claudia-Luminiţa Mihiţ et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to characterize a general property of -trichotomy through some Lyapunov functions for linear discrete-time systems in infinite dimensional spaces. Also, we apply the results to illustrate necessary and sufficient conditions for nonuniform exponential trichotomy and nonuniform polynomial trichotomy.