Designing a switching law for Mittag-Leffler stability in nonlinear singular fractional-order systems and its applications in synchronization

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-21 DOI:10.1016/j.cnsns.2024.108352

Duong Thi Hong , Do Duc Thuan , Nguyen Truong Thanh

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引用次数: 0

Abstract

In this work, the stability and synchronization issue of switched singular continuous-time fractional-order systems with nonlinear perturbation are examined. Using the fixed-point principle and S-procedure lemma, a sufficient condition for the existence and uniqueness of the solution to the switched singular fractional-order system is first stated. Next, using the Lyapunov functional method in combination with some techniques related to singular systems and fractional calculus, a switching rule for regularity, impulse-free, and Mittag-Leffler stability is developed based on the formation of a partition of the stability state regions in convex cones. For synchronizing switched fractional singular dynamical systems, we propose a state feedback controller that ensures regularity, impulse-free, and Mittag-Leffler stable in the error closed-loop system. Finally, the ease of use and computational convenience of our proposed methods are illustrated by two numerical examples and a practical example about DC motor controlling an inverted pendulum accompanied by simulation results.

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为非线性奇异分数阶系统的 Mittag-Leffler 稳定性设计开关定律及其在同步中的应用

本文研究了具有非线性扰动的切换奇异连续时间分数阶系统的稳定性和同步性问题。首先，利用定点原理和 S 过程两难定理，提出了开关奇异分数阶系统解存在性和唯一性的充分条件。接着，利用 Lyapunov 函数方法，结合奇异系统和分数微积分的一些相关技术，在形成凸锥形稳定状态区域分割的基础上，提出了正则性、无脉冲和 Mittag-Leffler 稳定性的切换规则。针对同步开关分数奇异动力学系统，我们提出了一种状态反馈控制器，可确保误差闭环系统的正则性、无脉冲和 Mittag-Leffler 稳定性。最后，我们通过两个数值示例和一个关于直流电机控制倒立摆的实际示例以及仿真结果，说明了我们提出的方法的易用性和计算便利性。

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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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.