随机非线性系统的实用定时Lyapunov判据及其应用

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-03 DOI:10.1016/j.cnsns.2024.108587

Jingjing You , Abudujelil Abudurahman , Shuxin Liu

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引用次数: 0

摘要

本文研究了随机非线性系统的实际定时概率稳定性。首先，利用随机微分方程理论和Lyapunov泛函方法建立了统一的PFxT-SP准则；在此基础上，建立了PFxT-SP的几种具体判断形式，并给出了相应的沉降时间（ST）估计。与一般的FxT-SP相比，PFxT-SP要求系统收敛到ST T内的一个特定区域，该区域和ST可以根据系统参数确定，与初始值无关。此外，给出了确定性系统的一个统一的实用定时稳定性判据和两个具体的判断。进一步研究了有扩散项和无扩散项的T-S模糊复杂网络的PFxT同步问题。最后通过仿真算例验证了理论结果的可行性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

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.