Stability analysis of gyroscopic systems with delay via decomposition

A. Yu Aleksandrov; A. P. Zhabko; Y. Chen

doi:10.1063/1.5034719

Stability analysis of gyroscopic systems with delay via decomposition

A. Yu Aleksandrov, A. P. Zhabko, Y. Chen

Research output › › peer-review

1 Citation (Scopus)

Abstract

A mechanical system describing by the second order linear differential equations with a positive parameter at the velocity forces and with time delay in the positional forces is studied. Using the decomposition method and Lyapunov-Krasovskii functionals, conditions are obtained under which from the asymptotic stability of two auxiliary first order subsystems it follows that, for sufficiently large values of the parameter, the original system is also asymptotically stable. Moreover, it is shown that the proposed approach can be applied to the stability investigation of linear gyroscopic systems with switched positional forces.

Original language	English
Title of host publication	EIGHTH POLYAKHOV'S READING
Subtitle of host publication	Proceedings of the International Scientific Conference on Mechanics
Editors	E Kustova, G Leonov, N Morosov, M Yushkov, M Mekhonoshina
Publisher	American Institute of Physics
Number of pages	6
Volume	1959
ISBN (Electronic)	9780735416604
ISBN (Print)	9780735416604
DOIs	https://doi.org/10.1063/1.5034719
Publication status	Published - 2 May 2018
Event	Восьмые Поляховские чтения: международная научная конференция по механике - Старый Петергоф, Saint Petersburg Duration: 29 Jan 2018 → 2 Feb 2018 Conference number: 8 https://events.spbu.ru/events/polyakhov_readings http://nanomat.spbu.ru/en/node/175 http://nanomat.spbu.ru/ru/node/192 http://spbu.ru/news-events/calendar/viii-polyahovskie-chteniya

Publication series

Name	AIP Conference Proceedings
Publisher	AMER INST PHYSICS
Volume	1959
ISSN (Print)	0094-243X

Conference

Conference	International Scientific Conference on Mechanics - Eighth Polyakhov's Reading
Country	Russian Federation
City	Saint Petersburg
Period	29/01/18 → 2/02/18
Internet address	https://events.spbu.ru/events/polyakhov_readings http://nanomat.spbu.ru/en/node/175 http://nanomat.spbu.ru/ru/node/192 http://spbu.ru/news-events/calendar/viii-polyahovskie-chteniya

Scopus subject areas

Physics and Astronomy(all)

Access to Document

10.1063/1.5034719

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Aleksandrov, A. Y., Zhabko, A. P., & Chen, Y. (2018). Stability analysis of gyroscopic systems with delay via decomposition. In E. Kustova, G. Leonov, N. Morosov, M. Yushkov, & M. Mekhonoshina (Eds.), EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics (Vol. 1959). [080002] (AIP Conference Proceedings; Vol. 1959). American Institute of Physics. https://doi.org/10.1063/1.5034719

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title = "Stability analysis of gyroscopic systems with delay via decomposition",

abstract = "A mechanical system describing by the second order linear differential equations with a positive parameter at the velocity forces and with time delay in the positional forces is studied. Using the decomposition method and Lyapunov-Krasovskii functionals, conditions are obtained under which from the asymptotic stability of two auxiliary first order subsystems it follows that, for sufficiently large values of the parameter, the original system is also asymptotically stable. Moreover, it is shown that the proposed approach can be applied to the stability investigation of linear gyroscopic systems with switched positional forces.",

keywords = "MECHANICAL SYSTEMS, HYBRID SYSTEMS",

author = "Aleksandrov, {A. Yu} and Zhabko, {A. P.} and Y. Chen",

year = "2018",

month = may,

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doi = "10.1063/1.5034719",

language = "English",

isbn = "9780735416604",

volume = "1959",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics",

editor = "E Kustova and G Leonov and N Morosov and M Yushkov and M Mekhonoshina",

booktitle = "EIGHTH POLYAKHOV'S READING",

address = "United States",

note = "International Scientific Conference on Mechanics - Eighth Polyakhov's Reading : 8th Polyakhov's Reading ; Conference date: 29-01-2018 Through 02-02-2018",

url = "https://events.spbu.ru/events/polyakhov_readings, http://nanomat.spbu.ru/en/node/175, http://nanomat.spbu.ru/ru/node/192, http://spbu.ru/news-events/calendar/viii-polyahovskie-chteniya",

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Aleksandrov, AY , Zhabko, AP & Chen, Y 2018, Stability analysis of gyroscopic systems with delay via decomposition. in E Kustova, G Leonov, N Morosov, M Yushkov & M Mekhonoshina (eds), EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics. vol. 1959, 080002, AIP Conference Proceedings, vol. 1959, American Institute of Physics, Восьмые Поляховские чтения, Saint Petersburg, 29/01/18. https://doi.org/10.1063/1.5034719

Stability analysis of gyroscopic systems with delay via decomposition. / Aleksandrov, A. Yu ; Zhabko, A. P.; Chen, Y.

EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics. ed. / E Kustova; G Leonov; N Morosov; M Yushkov; M Mekhonoshina. Vol. 1959 American Institute of Physics, 2018. 080002 (AIP Conference Proceedings; Vol. 1959).

Research output › › peer-review

TY - GEN

T1 - Stability analysis of gyroscopic systems with delay via decomposition

AU - Aleksandrov, A. Yu

AU - Zhabko, A. P.

AU - Chen, Y.

N1 - Conference code: 8

PY - 2018/5/2

Y1 - 2018/5/2

N2 - A mechanical system describing by the second order linear differential equations with a positive parameter at the velocity forces and with time delay in the positional forces is studied. Using the decomposition method and Lyapunov-Krasovskii functionals, conditions are obtained under which from the asymptotic stability of two auxiliary first order subsystems it follows that, for sufficiently large values of the parameter, the original system is also asymptotically stable. Moreover, it is shown that the proposed approach can be applied to the stability investigation of linear gyroscopic systems with switched positional forces.

AB - A mechanical system describing by the second order linear differential equations with a positive parameter at the velocity forces and with time delay in the positional forces is studied. Using the decomposition method and Lyapunov-Krasovskii functionals, conditions are obtained under which from the asymptotic stability of two auxiliary first order subsystems it follows that, for sufficiently large values of the parameter, the original system is also asymptotically stable. Moreover, it is shown that the proposed approach can be applied to the stability investigation of linear gyroscopic systems with switched positional forces.

KW - MECHANICAL SYSTEMS

KW - HYBRID SYSTEMS

UR - http://www.mendeley.com/research/stability-analysis-gyroscopic-systems-delay-via-decomposition

U2 - 10.1063/1.5034719

DO - 10.1063/1.5034719

M3 - Conference contribution

AN - SCOPUS:85047219289

SN - 9780735416604

VL - 1959

T3 - AIP Conference Proceedings

BT - EIGHTH POLYAKHOV'S READING

A2 - Kustova, E

A2 - Leonov, G

A2 - Morosov, N

A2 - Yushkov, M

A2 - Mekhonoshina, M

PB - American Institute of Physics

T2 - International Scientific Conference on Mechanics - Eighth Polyakhov's Reading

Y2 - 29 January 2018 through 2 February 2018

ER -

Aleksandrov AY , Zhabko AP, Chen Y. Stability analysis of gyroscopic systems with delay via decomposition. In Kustova E, Leonov G, Morosov N, Yushkov M, Mekhonoshina M, editors, EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics. Vol. 1959. American Institute of Physics. 2018. 080002. (AIP Conference Proceedings). https://doi.org/10.1063/1.5034719