Lyapunov Direct Method for Non-integer Order Systems

2015 ◽  
pp. 221-228
Author(s):  
Marta Zagórowska ◽  
Jerzy Baranowski ◽  
Waldemar Bauer ◽  
Tomasz Dziwiński ◽  
Paweł Piątek ◽  
...  
Keyword(s):  
Direct Method ◽  
Lyapunov Direct Method ◽  
Integer Order

Characterization of power systems near their stability boundary by Lyapunov direct method

2014 ◽  
Vol 47 (3) ◽  
pp. 9087-9092 ◽  
Author(s):  
Igor B. Yadykin ◽  
Dmitry E. Kataev ◽  
Alexey B. Iskakov ◽  
Vladislav K. Shipilov
Keyword(s):  
Power Systems ◽  
Direct Method ◽  
Stability Boundary ◽  
Lyapunov Direct Method

scholarly journals Stability of Fractional Differential Equations with New Generalized Hattaf Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Khalid Hattaf
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Direct Method ◽  
Lyapunov Direct Method ◽  
Science And Engineering ◽  
Fractional Differential ◽  
The Stability

This paper aims to study the stability of fractional differential equations involving the new generalized Hattaf fractional derivative which includes the most types of fractional derivatives with nonsingular kernels. The stability analysis is obtained by means of the Lyapunov direct method. First, some fundamental results and lemmas are established in order to achieve the goal of this study. Furthermore, the results related to exponential and Mittag–Leffler stability existing in recent studies are extended and generalized. Finally, illustrative examples are presented to show the applicability of our main results in some areas of science and engineering.

Design and stability analysis of interleaved flyback converter control using Lyapunov direct method with FPGA implementation

2020 ◽  
Vol 102 (3) ◽  
pp. 1651-1665
Author(s):  
Kanthimathi Raman ◽  
Kamala Jeyaraman ◽  
Saad Mekhilef ◽  
Lincy Grace Alexander
Keyword(s):  
Stability Analysis ◽  
Direct Method ◽  
Fpga Implementation ◽  
Lyapunov Direct Method ◽  
Flyback Converter

Adaptive impulsive synchronization for a class of fractional order complex chaotic systems

2019 ◽  
Vol 25 (10) ◽  
pp. 1614-1628 ◽  
Author(s):  
Xingpeng Zhang ◽  
Dong Li ◽  
Xiaohong Zhang
Keyword(s):  
Number Field ◽  
Fractional Order ◽  
Complex Number ◽  
Chaotic Systems ◽  
Direct Method ◽  
Order Complex ◽  
Lyapunov Direct Method ◽  
Impulsive Synchronization ◽  
Complex Chaotic Systems ◽  
Order Extension

In this paper, a new lemma is proposed to study the stability of a fractional order complex chaotic system without dividing the complex number into real and imaginary parts. The proving process of the new lemma combines the fundamental properties of the complex field and the fractional order extension of the Lyapunov direct method. It extends the fractional order extension of the Lyapunov direct method from the real number field to the complex number field. Based on the new lemma, we propose a new impulsive synchronization scheme for fractional order complex chaotic systems. The numerical simulation results also show the validity of our conclusion.

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

2017 ◽  
Vol 31 (05) ◽  
pp. 1750031 ◽  
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.

scholarly journals Stabilization of the FO-BLDCM Chaotic System in the Sense of Lyapunov

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Ping Zhou ◽  
Rongji Bai ◽  
Hao Cai
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Direct Method ◽  
Order System ◽  
Lyapunov Direct Method ◽  
Brushless Dc Motors ◽  
Brushless Dc ◽  
Dc Motors ◽  
System A ◽  
Control Scheme

Based on an integer-order Brushless DC motors (IO-BLDCM) system, we give a fractional-order Brushless DC motors (FO-BLDCM) system in this paper. There exists a chaotic attractor for fractional-order0.95<q≤1in the FO-BLDCM system. Furthermore, using the Lyapunov direct method for fractional-order system, a control scheme is proposed to stabilize the FO-BLDCM chaotic system in the sense of Lyapunov. Numerical simulation shows that the control scheme in this paper is valid for the FO-BLDCM chaotic system.

scholarly journals Stability for Caputo Fractional Differential Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Sung Kyu Choi ◽  
Bowon Kang ◽  
Namjip Koo
Keyword(s):  
Comparison Principle ◽  
Direct Method ◽  
Stability Of Solutions ◽  
Lyapunov Direct Method ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential

We introduce the notion ofh-stability for fractional differential systems. Then we investigate the boundedness andh-stability of solutions of Caputo fractional differential systems by using fractional comparison principle and fractional Lyapunov direct method. Furthermore, we give examples to illustrate our results.

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