Fixed-time stability theorem of stochastic nonlinear systems

To solve the fixed-time stability problem for stochastic systems, which has not been investigated due to the difficulty caused by the existence of stochastic, the fixed-time stability is investigated for stochastic nonlinear systems described by the It differential equation in this note. The main co...

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Published inInternational journal of control Vol. 92; no. 9; pp. 2194 - 2200
Main Authors Yu, Jiaju, Yu, Shuanghe, Li, Juan, Yan, Yan
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.09.2019
Taylor & Francis Ltd
Subjects
Differential equations
fixed-time stability
infinitesimal generator
Lyapunov function
Nonlinear systems
Probability theory
Stability
stochastic nonlinear systems
stochastic settling time function
Stochastic systems
Theorems
Online AccessGet full text
ISSN0020-7179
1366-5820
DOI10.1080/00207179.2018.1430900

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Abstract To solve the fixed-time stability problem for stochastic systems, which has not been investigated due to the difficulty caused by the existence of stochastic, the fixed-time stability is investigated for stochastic nonlinear systems described by the It differential equation in this note. The main contributions exist in: (1) A new concept, fixed-time stable in probability, is proposed, and the detailed definition is given. (2) A criterion theorem is proposed to judge the fixed-time stable in probability, in addition, several corollaries are given for proving the fixed-time stability in probability for stochastic nonlinear systems. Two simulation examples are given to verify the proposed theoretical results in this paper.
AbstractList To solve the fixed-time stability problem for stochastic systems, which has not been investigated due to the difficulty caused by the existence of stochastic, the fixed-time stability is investigated for stochastic nonlinear systems described by the It [Formula omitted.] differential equation in this note. The main contributions exist in: (1) A new concept, fixed-time stable in probability, is proposed, and the detailed definition is given. (2) A criterion theorem is proposed to judge the fixed-time stable in probability, in addition, several corollaries are given for proving the fixed-time stability in probability for stochastic nonlinear systems. Two simulation examples are given to verify the proposed theoretical results in this paper.
To solve the fixed-time stability problem for stochastic systems, which has not been investigated due to the difficulty caused by the existence of stochastic, the fixed-time stability is investigated for stochastic nonlinear systems described by the It differential equation in this note. The main contributions exist in: (1) A new concept, fixed-time stable in probability, is proposed, and the detailed definition is given. (2) A criterion theorem is proposed to judge the fixed-time stable in probability, in addition, several corollaries are given for proving the fixed-time stability in probability for stochastic nonlinear systems. Two simulation examples are given to verify the proposed theoretical results in this paper.
Author Yu, Jiaju
Li, Juan
Yan, Yan
Yu, Shuanghe
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Snippet To solve the fixed-time stability problem for stochastic systems, which has not been investigated due to the difficulty caused by the existence of stochastic,...
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SubjectTerms Differential equations
fixed-time stability
infinitesimal generator
Lyapunov function
Nonlinear systems
Probability theory
Stability
stochastic nonlinear systems
stochastic settling time function
Stochastic systems
Theorems
Title Fixed-time stability theorem of stochastic nonlinear systems
URI https://www.tandfonline.com/doi/abs/10.1080/00207179.2018.1430900
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