Stability Analysis of Fractional-Order Nonlinear Systems with Delay

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.

Download Full-text

Global stabilization of memristor-based fractional-order neural networks with delay via output-feedback control

Modern Physics Letters B ◽

10.1142/s0217984917500312 ◽

2017 ◽

Vol 31 (05) ◽

pp. 1750031 ◽

Cited By ~ 13

Author(s):

Jiyang Chen ◽

Chuandong Li ◽

Tingwen Huang ◽

Xujun Yang

Keyword(s):

Neural Networks ◽

Fractional Order ◽

Output Feedback ◽

Differential Inclusions ◽

Direct Method ◽

Sufficient Conditions ◽

Output Feedback Control ◽

Global Stabilization ◽

Lyapunov Direct Method ◽

Stabilizing Control

In this paper, the memristor-based fractional-order neural networks (MFNN) with delay and with two types of stabilizing control are described in detail. Based on the Lyapunov direct method, the theories of set-value maps, differential inclusions and comparison principle, some sufficient conditions and assumptions for global stabilization of this neural network model are established. Finally, two numerical examples are presented to demonstrate the effectiveness and practicability of the obtained results.

Download Full-text

Stability analysis of conformable fractional-order nonlinear systems depending on a parameter

Journal of Applied Analysis ◽

10.1515/jaa-2020-2025 ◽

2020 ◽

Vol 26 (2) ◽

pp. 287-296

Author(s):

O. Naifar ◽

G. Rebiai ◽

A. Ben Makhlouf ◽

M. A. Hammami ◽

A. Guezane-Lakoud

Keyword(s):

Stability Analysis ◽

Nonlinear Systems ◽

Fractional Order ◽

Feedback Controller ◽

Fractional Order Systems ◽

The Stability

AbstractIn this paper, the stability of conformable fractional-order nonlinear systems depending on a parameter is presented and described. Furthermore, The design of a feedback controller for the same class of conformable fractional-order systems is introduced. Illustrative examples are given at the end of the paper to show the effectiveness of the proposed results.

Download Full-text

Synchronization of the Fractional-Order Brushless DC Motors Chaotic System

Journal of Control Science and Engineering ◽

10.1155/2016/1236210 ◽

2016 ◽

Vol 2016 ◽

pp. 1-5 ◽

Cited By ~ 1

Author(s):

Shiyun Shen ◽

Ping Zhou

Keyword(s):

Fractional Order ◽

Chaotic System ◽

Chaos Synchronization ◽

Direct Method ◽

Fractional Order Systems ◽

Lyapunov Direct Method ◽

Brushless Dc Motors ◽

Brushless Dc ◽

Dc Motors ◽

Synchronization Scheme

Based on the extension of Lyapunov direct method for nonlinear fractional-order systems, chaos synchronization for the fractional-order Brushless DC motors (BLDCM) is discussed. A chaos synchronization scheme is suggested. By means of Lyapunov candidate function, the theoretical proof of chaos synchronization is addressed. The numerical results show that the chaos synchronization scheme is valid.

Download Full-text

Stability of a Class of Fractional-Order Nonlinear Systems

Discrete Dynamics in Nature and Society ◽

10.1155/2014/724270 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14 ◽

Cited By ~ 6

Author(s):

Tianzeng Li ◽

Yu Wang

Keyword(s):

Stability Analysis ◽

Nonlinear Systems ◽

Asymptotic Stability ◽

Numerical Simulations ◽

Fractional Order ◽

Sufficient Conditions ◽

Gronwall Inequality ◽

Globally Asymptotic Stability ◽

Grönwall Inequality ◽

Two Systems

In this letter stability analysis of fractional order nonlinear systems is studied. Some new sufficient conditions on the local (globally) asymptotic stability for a class of fractional order nonlinear systems with order0<α<2are proposed by using properties of Mittag-Leffler function and the Gronwall inequality. And the corresponding stabilization criteria are also given. The numerical simulations of two systems with order0<α<1and two systems with order1<α<2illustrate the effectiveness and universality of the proposed approach.

Download Full-text

Stability of fractional-order nonlinear systems by Lyapunov direct method

IET Control Theory and Applications ◽

10.1049/iet-cta.2018.5233 ◽

2018 ◽

Vol 12 (17) ◽

pp. 2417-2422 ◽

Cited By ~ 23

Author(s):

Hoang T. Tuan ◽

Hieu Trinh

Keyword(s):

Nonlinear Systems ◽

Fractional Order ◽

Direct Method ◽

Lyapunov Direct Method

Download Full-text

Preservation of Stability and Synchronization of a Class of Fractional-Order Systems

Mathematical Problems in Engineering ◽

10.1155/2012/928930 ◽

2012 ◽

Vol 2012 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

Armando Fabián Lugo-Peñaloza ◽

José Job Flores-Godoy ◽

Guillermo Fernández-Anaya

Keyword(s):

Nonlinear Systems ◽

Fractional Order ◽

Linear Part ◽

Autonomous Systems ◽

Sufficient Conditions ◽

Fractional Order Systems ◽

Nonlinear Part ◽

Fractional Differential ◽

Linear And Nonlinear ◽

Linear And Nonlinear Systems

We present sufficient conditions for the preservation of stability of fractional-order systems, and then we use this result to preserve the synchronization, in a master-slave scheme, of fractional-order systems. The systems treated herein are autonomous fractional differential linear and nonlinear systems with commensurate orders lying between 0 and 2, where the nonlinear ones can be described as a linear part plus a nonlinear part. These results are based on stability properties for equilibria of fractional-order autonomous systems and some similar properties for the preservation of stability in integer order systems. Some simulation examples are presented only to show the effectiveness of the analytic result.

Download Full-text