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

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  • Michał Niezabitowski

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.

Suggested Citation

  • Michał Niezabitowski, 2016. "On the Sequences Realizing Perron and Lyapunov Exponents of Discrete Linear Time-Varying Systems," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-7, November.
    • Handle: RePEc:hin:jnlmpe:1487824
    DOI: 10.1155/2016/1487824
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