Stability Analysis of Fractional-Order Nonlinear Systems with Delay

Yu Wang; Tianzeng Li

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Stability Analysis of Fractional-Order Nonlinear Systems with Delay

机译：分数阶时滞非线性系统的稳定性分析

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Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.

机译：研究了分数阶时滞非线性系统的稳定性。我们提出了时滞系统的Mittag-Leffler稳定性的定义，并利用Mittag-Leffler函数的性质和Laplace变换介绍了分数Lyapunov直接法。然后提出了一些新的充分条件，该条件保证了时滞分数阶非线性系统的渐近稳定性。并通过分数比较原理和Caputo分数阶系统扩展了Riemann-Liouville分数阶系统的应用。算例仿真表明了该方法的通用性和有效性。

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《Mathematical Problems in Engineering》 |2014年第8期|301235.1-301235.8|共8页
作者
Yu Wang; Tianzeng Li;
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School of Science, Sichuan University of Science and Engineering, Zigong 643000, China,Sichuan Province University Key Laboratory of Bridge Non-Destruction Detecting and Engineering Computing, Sichuan University of Science and Engineering, Zigong 643000, China;

School of Science, Sichuan University of Science and Engineering, Zigong 643000, China,Sichuan Province University Key Laboratory of Bridge Non-Destruction Detecting and Engineering Computing, Sichuan University of Science and Engineering, Zigong 643000, China;

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1. Stability analysis for a class of fractional-order nonlinear systems with time-varying delays [J] . Rahmanipour Pourya, Ghadiri Hamid Soft computing: A fusion of foundations, methodologies and applications . 2020,第22期

机译：具有时变延迟的一类分数级非线性系统的稳定性分析
2. Stability analysis for a class of fractional-order nonlinear systems with time-varying delays (Jul, 10.1007/s00500-020-05118-w, 2020) [J] . Rahmanipour Pourya, Ghadiri Hamid Soft computing: A fusion of foundations, methodologies and applications . 2020,第22期

机译：具有时变延迟的一类分数级非线性系统的稳定性分析（JUL，10.1007 / S00500-020-05118-W，2020）
3. Stability Analysis of Fractional-Order Nonlinear Systems with Delay [J] . YuWang, TianzengLi Mathematical Problems in Engineering: Theory, Methods and Applications . 2014,第a期

机译：延迟延迟分数非线性系统的稳定性分析
4. Stability region of fractional-order PI ^#x03BB;D^#x03BC; controller for fractional-order systems with time delay [C] . Wu Qunhong, Ou Linlin, Ni Hongjie, International Conference on Control, Automation, Robotics Vision . 2012

机译：具有时滞的分数阶系统的分数阶PI ^{λ D ^{μ控制器的稳定性区域}}
5. Stability and Control of Fractional-Order Systems with Delays and Periodic Coefficients [D] . Dabiri, Arman. 2018

机译：具有时滞和周期系数的分数阶系统的稳定性和控制
6. Stability analysis of the hiv model through incommensurate fractional-order nonlinear system [O] . Bahatdin DAŞBAŞI -1

机译：通过不等分数阶非线性系统分析hiv模型的稳定性
7. Correction to: Stability analysis for a class of fractional-order nonlinear systems with time-varying delays [O] . Pourya Rahmanipour, Hamid Ghadiri 2020

机译：校正：具有时变延迟的一类小数非线性系统的稳定性分析

Stability Analysis of Fractional-Order Nonlinear Systems with Delay

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