Lyapunov function method for investigation of stability of stochastic Ito random-structure systems with impulse Markov switchings. I. General theorems on the stability of stochastic impulse systems

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

doi:10.1007/s10559-009-9102-8

Lyapunov function method for investigation of stability of stochastic Ito random-structure systems with impulse Markov switchings. I. General theorems on the stability of stochastic impulse systems

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

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

The asymptotic stochastic stability on the whole and asymptotic p-stability on the whole are investigated with the help of Lyapunov functions and the concept of 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 constant perturbations is considered.

Original language	English
Pages (from-to)	281-290
Number of pages	10
Journal	Cybernetics and Systems Analysis
Volume	45
Issue number	2
DOIs	https://doi.org/10.1007/s10559-009-9102-8
Publication status	Published - 2009
Externally published	Yes

Keywords

Asymptotic stability
Asymptotic stability in probability
Autonomous system
Exponential stability
Markov switching
P-stability
Stabilityin probability
Stochastic dynamic system

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10.1007/s10559-009-9102-8

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abstract = "The asymptotic stochastic stability on the whole and asymptotic p-stability on the whole are investigated with the help of Lyapunov functions and the concept of 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 constant perturbations is considered.",

keywords = "Asymptotic stability, Asymptotic stability in probability, Autonomous system, Exponential stability, Markov switching, P-stability, Stabilityin probability, Stochastic dynamic system",

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

year = "2009",

doi = "10.1007/s10559-009-9102-8",

language = "English",

volume = "45",

pages = "281--290",

journal = "Cybernetics and Systems Analysis",

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Lyapunov function method for investigation of stability of stochastic Ito random-structure systems with impulse Markov switchings. I. General theorems on the stability of stochastic impulse systems. / Lukashiv, T. O.; Yurchenko, I. V.; Yasinskii, V. K.
In: Cybernetics and Systems Analysis, Vol. 45, No. 2, 2009, p. 281-290.

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. I. General theorems on the stability of stochastic impulse systems

AU - Lukashiv, T. O.

AU - Yurchenko, I. V.

AU - Yasinskii, V. K.

PY - 2009

Y1 - 2009

N2 - The asymptotic stochastic stability on the whole and asymptotic p-stability on the whole are investigated with the help of Lyapunov functions and the concept of 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 constant perturbations is considered.

AB - The asymptotic stochastic stability on the whole and asymptotic p-stability on the whole are investigated with the help of Lyapunov functions and the concept of 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 constant perturbations is considered.

KW - Asymptotic stability

KW - Asymptotic stability in probability

KW - Autonomous system

KW - Exponential stability

KW - Markov switching

KW - P-stability

KW - Stabilityin probability

KW - Stochastic dynamic system

UR - https://www.scopus.com/pages/publications/67349171585

U2 - 10.1007/s10559-009-9102-8

DO - 10.1007/s10559-009-9102-8

M3 - Article

AN - SCOPUS:67349171585

SN - 1060-0396

VL - 45

SP - 281

EP - 290

JO - Cybernetics and Systems Analysis

JF - Cybernetics and Systems Analysis

IS - 2

ER -

Lyapunov function method for investigation of stability of stochastic Ito random-structure systems with impulse Markov switchings. I. General theorems on the stability of stochastic impulse systems

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Keywords

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