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Avtomatika i Telemekhanika, 2017, Issue 10, Pages 33–54 (Mi at14901)  
Nonlinear Systems

Application of the Lyapunov vector functions to the stability study of fixed points in the sets of discrete dynamic systems

V. I. Slyn'ko

Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine
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Abstract: Stability conditions for fixed points of the dynamic systems in the space of nonempty convex compacts in finite-dimensional space were obtained. For the sets of dynamic systems, a methods was proposed to construct the Lyapunov vector functions. The study was carried out using the Matrosov method of comparison in combination with the methods of the convex geometry. In some special cases, the results obtained are applicable to the study of the sets of trajectories of dynamic systems.
Keywords: comparison method, discrete dynamic system, mixed volumes, Lyapunov vector function.
Funding agency Grant number
Ministry of Education and Science of Ukraine 0116U004691
This work was supported in part by the Ukrainian Ministry of Education and Science, project no. 0116U004691.
Presented by the member of Editorial Board: S. N. Vassilyev

Received: 11.06.2015
English version:
Automation and Remote Control, 2017, Volume 78, Issue 10, Pages 1757–1774
DOI: https://doi.org/10.1134/S0005117917100022
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. I. Slyn'ko, “Application of the Lyapunov vector functions to the stability study of fixed points in the sets of discrete dynamic systems”, Avtomat. i Telemekh., 2017, no. 10, 33–54; Autom. Remote Control, 78:10 (2017), 1757–1774
Citation in format AMSBIB
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