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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 12, Pages 12–18 (Mi ivm9181)  
This article is cited in 5 scientific papers (total in 5 papers)

On a method of evaluation of attraction domain for fixed point of nonlinear point mapping of arbitrary dimension

O. G. Antonovskayaa, V. I. Goryunovb

a University of Architecture and Civil Engineering, 65 Alekseevskaya str., Nizhny Novgorod, 603950 Russia
b Nizhny Novgorod State University, 23 Gagarin Ave., Nizhny Novgorod, 603950 Russia
Full-text PDF (167 kB) Citations (5)
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Abstract: In this paper we describe the method of attraction domain evaluation for equilibrium states of nonlinear discrete dynamic system based on Lyapunov functions method. Attraction domain evaluation size is equilibrium state neighborhood where the first difference of Lyapunov function is negative. Lyapunov function is chosen as positive quadratic form for which the negativity of its first difference by virtue of linearized system is guaranteed with given supply. We propose the method of attraction domain extension.
Keywords: discrete dynamic system, macro-structure of state space, Lyapunov function method.
Received: 06.05.2015
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 12, Pages 9–14
DOI: https://doi.org/10.3103/S1066369X16120021
Bibliographic databases:
Document Type: Article
UDC: 517.968
Language: Russian
Citation: O. G. Antonovskaya, V. I. Goryunov, “On a method of evaluation of attraction domain for fixed point of nonlinear point mapping of arbitrary dimension”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 12, 12–18; Russian Math. (Iz. VUZ), 60:12 (2016), 9–14
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/ivm9181
  • https://www.mathnet.ru/eng/ivm/y2016/i12/p12
    • This publication is cited in the following 5 articles:
    1. A. V. Besklubnaya, O. G. Antonovskaya, “O sokhranenii kvadratichnoi funktsii Lyapunova lineinoi diskretnoi sistemy pri statsionarnykh vozmuscheniyakh koeffitsientov sistemy”, Mezhdunar. nauch.-issled. zhurn., 2024, no. 2(140), 1–6  mathnet  crossref
    2. O. G. Antonovskaya, “On the Preservation of a Quadratic Lyapunov Function of a Linear Differential Autonomous System under Constant Perturbations of the Coefficients”, Diff Equat, 59:3 (2023), 293  crossref
    3. O. G. Antonovskaya, “On the Study of Robust Exponential Stability of Continuous- and Discrete-Time Systems”, Diff Equat, 59:4 (2023), 452  crossref
    4. O. G. Antonovskaya, “Application of quadratic Lyapunov functions to investigation of stability of systems with delay”, Russian Math. (Iz. VUZ), 63:10 (2019), 13–17  mathnet  crossref  crossref  isi
    5. O. G. Antonovskaya, “Primenenie kvadratichnykh funktsii Lyapunova pri reshenii prikladnykh dinamicheskikh zadach”, Mezhdunar. nauch.-issled. zhurn., 2017, no. 8-2(62), 142–147  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:61
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