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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 1487824, 7 pages
http://dx.doi.org/10.1155/2016/1487824
Research Article

On the Sequences Realizing Perron and Lyapunov Exponents of Discrete Linear Time-Varying Systems

Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, Akademicka 16 Street, 44-100 Gliwice, Poland

Received 29 July 2016; Accepted 12 October 2016

Academic Editor: Sotiris K. Ntouyas

Copyright © 2016 Michał Niezabitowski. 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

We investigate properties of partial exponents (in particular, the Lyapunov and Perron exponents) of discrete time-varying linear systems. In the set of all increasing sequences of natural numbers, we define an equivalence relation with the property that sequences in the same equivalence class have the same partial exponent. We also define certain subclass of all increasing sequences of natural numbers, including all arithmetic sequences, such that all partial exponents are achievable on a sequence from this class. Finally, we show that the Perron and Lyapunov exponents may be approximated by partial exponents achievable on sequences in certain sense similar to geometric sequences.