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On stability and stabilization of some discrete dynamical systems
Author(s) -
Čermák Jan,
Jánský Jiří,
Matsunaga Hideaki
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4855
Subject(s) - mathematics , dynamical systems theory , stability (learning theory) , simple (philosophy) , decomposition , discrete system , polynomial , integer (computer science) , discrete time and continuous time , control theory (sociology) , mathematical optimization , mathematical analysis , computer science , algorithm , control (management) , statistics , ecology , philosophy , physics , epistemology , quantum mechanics , machine learning , artificial intelligence , biology , programming language
The paper formulates effective and nonimprovable stability conditions for a linear difference system involving 2 integer delays. The used technique combines algorithm of the discrete D‐decomposition method with some procedures of the polynomial theory. Contrary to the related existing results, the derived conditions are fully explicit with respect to both delays, which enables their simple applicability in various scientific and engineering areas. As an illustration, we show their importance in delayed feedback controls of discrete dynamical systems, with a particular emphasis put on stabilization of unstable steady states of the discrete logistic map.