Abstract
A class of two-parameter discrete systems defined on the ring \(\mathbb{Z}_m = {\mathbb{Z} \mathord{\left/ {\vphantom {\mathbb{Z} {(m)}}} \right. \kern-\nulldelimiterspace} {(m)}}{\text{ }}\) of class of residues of integers \(\mathbb{Z}\) modulo m is studied. All solutions are shown to be periodic, stability conditions (equality of solutions to zero, beginning from a certain instant) and a controllability condition are formulated. Controllability is shown to guarantee stabilizability.
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Gaishun, I.V. Two-Parameter Discrete Systems over a Residue Ring and Their Properties. Automation and Remote Control 63, 1717–1723 (2002). https://doi.org/10.1023/A:1020943028933
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DOI: https://doi.org/10.1023/A:1020943028933