Abstract
For a shift operator in the space of bounded sequences, we prove an analog of the classical Perron theorem on the spectrum of a positive matrix, which is then used to study the asymptotic properties of two-parameter discrete systems with nonnegative coefficients.
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Kaczorek, T., Two-Dimensional Linear Systems, Berlin, 1985.
Gaishun, I.V., Mnogoparametricheskie sistemy upravleniya (Multiparameter Control Systems), Minsk: Navuka i Tekhnika, 1996.
Bellman, R., Introduction to Matrix Analysis, New York–Toronto–London: McGraw-Hill Book Co.,1960. Translated under the title Vvedenie v teoriyu matrits, Moscow: Izdat. “Nauka,” 1969.
Horn, R.A. and Johnson, C.R., Matrix Analysis, Cambridge: Cambridge Univ. Press, 1985. Translatedunder the title Matrichnyi analiz, Moscow: Mir, 1989.
Krasnosel’skii, M.A., Polozhitel’nye resheniya operatornykh uravnenii (Positive Solutions of OperatorEquations), Moscow: Gosudarstv. Izdat. Fiz.-Mat. Lit., 1962.
Gaishun, I.V., Sistemy s diskretnym vremenem (Systems with Discrete Time), Minsk, 2001.
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Original Russian Text © I.V. Gaishun, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 5, pp. 578–583.
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Gaishun, I.V. Stability of two-parameter discrete systems with nonnegative coefficients. Diff Equat 51, 586–591 (2015). https://doi.org/10.1134/S001226611505002X
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DOI: https://doi.org/10.1134/S001226611505002X