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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Bibliographic Details
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
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ISSN0020-7179
1366-5820
DOI10.1080/00207179.2018.1430900

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Summary: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.
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ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2018.1430900