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Avtomatika i Telemekhanika, 2020, Issue 2, Pages 62–75
DOI: https://doi.org/10.31857/S0005231020020051 (Mi at15449) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Nonlinear Systems

Divergent stability conditions of dynamic systems

I. B. Furtatab

a Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
b ITMO University, St. Petersburg, Russia
Full-text PDF (962 kB) Citations (8)
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DOI: https://doi.org/10.31857/S0005231020020051
Abstract: A new method for analyzing the stability of dynamic systems using the properties of the flow and divergence of the phase vector is proposed. A relation between Lyapunov's function method and this method is established. Based on the results obtained below, a design procedure of state feedback control laws for stabilizing dynamic systems is developed. The control law design is reduced to solving a differential inequality with respect to the control function desired. Examples illustrating the applicability of the new and existing methods are considered.
Keywords: dynamic system, stability, flow of a vector field, divergence, control.
Funding agency Grant number
Russian Foundation for Basic Research 17-08-01266_а
Russian Science Foundation 18-79-10104
The results of Section 2 were obtained under support of the Russian Foundation for Basic Research in IPME RAS, project no. 17-08-01266. The results of Section 3 were obtained under support of the Russian Science Foundation in IPME RAS, project no. 18-79-10104.
Presented by the member of Editorial Board: L. B. Rapoport

Received: 21.05.2019
Revised: 02.07.2019
Accepted: 18.07.2019
English version:
Automation and Remote Control, 2020, Volume 81, Issue 2, Pages 247–257
DOI: https://doi.org/10.1134/S0005117920020058
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. B. Furtat, “Divergent stability conditions of dynamic systems”, Avtomat. i Telemekh., 2020, no. 2, 62–75; Autom. Remote Control, 81:2 (2020), 247–257
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/at/y2020/i2/p62
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:35
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