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Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimir: 1064-2315
ISSN On-line: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v33.i5-8.20
9 pages

Minimal Invariant Sets of Discrete Dynamic Systems with a Stable Linear Part

Vsevolod M. Kuntsevich
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev, Ukraine
Boris N. Pshenitchnyi
V.M.Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kyiv

RESUMO

The paper concerns analysis of asymptotic properties of the two classes of discrete systems with a stable linear part: i) non-autonomous linear systems under bounded set-estimated disturbances and ii) autonomous nonlinear systems with bounded nonlinear part, particularly, relay systems. For these two classes, the problem of calculating their invariant sets, the dissipativity problem, has been solved. For relay systems, all regular trajectories, which are inside their invariant sets, have been proven to approach the stable limit cycles. It has been proven also that a minimal invariant set may contain a number of stationary sets, stable stationary points and stable limit cycles in particular.


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