{"title":"随机非线性系统的实用定时Lyapunov判据及其应用","authors":"Jingjing You, Abudujelil Abudurahman, Shuxin Liu","doi":"10.1016/j.cnsns.2024.108587","DOIUrl":null,"url":null,"abstract":"This article investigates the practical fixed-time stability in probability (PFxT-SP) of stochastic nonlinear systems (SNS). First, a unified PFxT-SP criterion is developed by using the stochastic differential equation theory and Lyapunov functional method. Building on this foundation, several specific judgment forms of the PFxT-SP are established and corresponding estimates for the settling times (ST) are obtained. Compared to general FxT-SP, PFxT-SP requires the system to converge to a specific region within ST <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mi>T</mml:mi></mml:math>, where the region and ST can be determined based on the system parameters, and they are independent of the initial values. Additionally, a unified practical fixed-time stability (PFxT-S) criterion of deterministic systems and two specific judgments are presented. Furthermore, the PFxT synchronization of T-S fuzzy complex networks with and without diffusion term is investigated. Finally, the feasibility of the theoretical results are illustrated by some simulation examples.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"37 1","pages":""},"PeriodicalIF":3.4000,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Practical fixed-time Lyapunov criterion of stochastic nonlinear systems and its application\",\"authors\":\"Jingjing You, Abudujelil Abudurahman, Shuxin Liu\",\"doi\":\"10.1016/j.cnsns.2024.108587\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article investigates the practical fixed-time stability in probability (PFxT-SP) of stochastic nonlinear systems (SNS). First, a unified PFxT-SP criterion is developed by using the stochastic differential equation theory and Lyapunov functional method. Building on this foundation, several specific judgment forms of the PFxT-SP are established and corresponding estimates for the settling times (ST) are obtained. Compared to general FxT-SP, PFxT-SP requires the system to converge to a specific region within ST <mml:math altimg=\\\"si1.svg\\\" display=\\\"inline\\\"><mml:mi>T</mml:mi></mml:math>, where the region and ST can be determined based on the system parameters, and they are independent of the initial values. Additionally, a unified practical fixed-time stability (PFxT-S) criterion of deterministic systems and two specific judgments are presented. Furthermore, the PFxT synchronization of T-S fuzzy complex networks with and without diffusion term is investigated. Finally, the feasibility of the theoretical results are illustrated by some simulation examples.\",\"PeriodicalId\":50658,\"journal\":{\"name\":\"Communications in Nonlinear Science and Numerical Simulation\",\"volume\":\"37 1\",\"pages\":\"\"},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2025-01-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Nonlinear Science and Numerical Simulation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1016/j.cnsns.2024.108587\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.cnsns.2024.108587","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Practical fixed-time Lyapunov criterion of stochastic nonlinear systems and its application
This article investigates the practical fixed-time stability in probability (PFxT-SP) of stochastic nonlinear systems (SNS). First, a unified PFxT-SP criterion is developed by using the stochastic differential equation theory and Lyapunov functional method. Building on this foundation, several specific judgment forms of the PFxT-SP are established and corresponding estimates for the settling times (ST) are obtained. Compared to general FxT-SP, PFxT-SP requires the system to converge to a specific region within ST T, where the region and ST can be determined based on the system parameters, and they are independent of the initial values. Additionally, a unified practical fixed-time stability (PFxT-S) criterion of deterministic systems and two specific judgments are presented. Furthermore, the PFxT synchronization of T-S fuzzy complex networks with and without diffusion term is investigated. Finally, the feasibility of the theoretical results are illustrated by some simulation examples.
期刊介绍：
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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