Lyapunov function method for investigation of stability of stochastic ito random-structure systems with impulse markov switchings. II. First-approximation stability of stochastic impulse systems with markov parameters

T. O. Lukashiv; I. V. Yurchenko; V. K. Yasinsky

doi:10.1007/s10559-009-9109-1

Lyapunov function method for investigation of stability of stochastic ito random-structure systems with impulse markov switchings. II. First-approximation stability of stochastic impulse systems with markov parameters

T. O. Lukashiv^*, I. V. Yurchenko, V. K. Yasinsky

^*Corresponding author for this work

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

Abstract

The asymptotic stochastic stability in the large and asymptotic p-stability in the large are investigated with the help of the Lyapunov functions and an infinitesimal operator over solutions to a system (to calculate this operator, it suffices to know only the coefficients of the system). The stability under persistent disturbances is considered.

Original language	English
Pages (from-to)	464-476
Number of pages	13
Journal	Cybernetics and Systems Analysis
Volume	45
Issue number	3
DOIs	https://doi.org/10.1007/s10559-009-9109-1
Publication status	Published - 2009
Externally published	Yes

Keywords

Asymptotic stability
Asymptotic stability in probability
Autonomous system
Exponential stability
P-stability
Stability in probability
Stochastic dynamic system

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Lukashiv, T. O., Yurchenko, I. V., & Yasinsky, V. K. (2009). Lyapunov function method for investigation of stability of stochastic ito random-structure systems with impulse markov switchings. II. First-approximation stability of stochastic impulse systems with markov parameters. Cybernetics and Systems Analysis, 45(3), 464-476. https://doi.org/10.1007/s10559-009-9109-1

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abstract = "The asymptotic stochastic stability in the large and asymptotic p-stability in the large are investigated with the help of the Lyapunov functions and an infinitesimal operator over solutions to a system (to calculate this operator, it suffices to know only the coefficients of the system). The stability under persistent disturbances is considered.",

keywords = "Asymptotic stability, Asymptotic stability in probability, Autonomous system, Exponential stability, P-stability, Stability in probability, Stochastic dynamic system",

author = "Lukashiv, {T. O.} and Yurchenko, {I. V.} and Yasinsky, {V. K.}",

year = "2009",

doi = "10.1007/s10559-009-9109-1",

language = "English",

volume = "45",

pages = "464--476",

journal = "Cybernetics and Systems Analysis",

issn = "1060-0396",

publisher = "Springer New York",

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Lukashiv, TO, Yurchenko, IV & Yasinsky, VK 2009, 'Lyapunov function method for investigation of stability of stochastic ito random-structure systems with impulse markov switchings. II. First-approximation stability of stochastic impulse systems with markov parameters', Cybernetics and Systems Analysis, vol. 45, no. 3, pp. 464-476. https://doi.org/10.1007/s10559-009-9109-1

Lyapunov function method for investigation of stability of stochastic ito random-structure systems with impulse markov switchings. II. First-approximation stability of stochastic impulse systems with markov parameters. / Lukashiv, T. O.; Yurchenko, I. V.; Yasinsky, V. K.
In: Cybernetics and Systems Analysis, Vol. 45, No. 3, 2009, p. 464-476.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Lyapunov function method for investigation of stability of stochastic ito random-structure systems with impulse markov switchings. II. First-approximation stability of stochastic impulse systems with markov parameters

AU - Lukashiv, T. O.

AU - Yurchenko, I. V.

AU - Yasinsky, V. K.

PY - 2009

Y1 - 2009

N2 - The asymptotic stochastic stability in the large and asymptotic p-stability in the large are investigated with the help of the Lyapunov functions and an infinitesimal operator over solutions to a system (to calculate this operator, it suffices to know only the coefficients of the system). The stability under persistent disturbances is considered.

AB - The asymptotic stochastic stability in the large and asymptotic p-stability in the large are investigated with the help of the Lyapunov functions and an infinitesimal operator over solutions to a system (to calculate this operator, it suffices to know only the coefficients of the system). The stability under persistent disturbances is considered.

KW - Asymptotic stability

KW - Asymptotic stability in probability

KW - Autonomous system

KW - Exponential stability

KW - P-stability

KW - Stability in probability

KW - Stochastic dynamic system

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U2 - 10.1007/s10559-009-9109-1

DO - 10.1007/s10559-009-9109-1

M3 - Article

AN - SCOPUS:67649414914

SN - 1060-0396

VL - 45

SP - 464

EP - 476

JO - Cybernetics and Systems Analysis

JF - Cybernetics and Systems Analysis

IS - 3

ER -

Lyapunov function method for investigation of stability of stochastic ito random-structure systems with impulse markov switchings. II. First-approximation stability of stochastic impulse systems with markov parameters

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Keywords

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