Stability Preservation Analysis for Frequency-Based Methods in Numerical Simulation of Fractional Order Systems

2009 ◽  
Vol 47 (1) ◽  
pp. 321-338 ◽  
Author(s):  
Mohammad Saleh Tavazoei ◽  
Mohammad Haeri ◽  
Sadegh Bolouki ◽  
Milad Siami
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Fractional Order Systems

LAG SYNCHRONIZATION OF THE FRACTIONAL-ORDER SYSTEM VIA NONLINEAR OBSERVER

2011 ◽  
Vol 25 (29) ◽  
pp. 3951-3964 ◽  
Author(s):  
HAO ZHU ◽  
ZHONGSHI HE ◽  
SHANGBO ZHOU
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Stability Theorem ◽  
Nonlinear Observer ◽  
Order System ◽  
Fractional Order Systems ◽  
Lag Synchronization ◽  
Systematic Method ◽  
Fractional System ◽  
The Stability

In this paper, based on the idea of nonlinear observer, lag synchronization of chaotic fractional system with commensurate and incommensurate order is studied by the stability theorem of linear fractional-order systems. The theoretical analysis of fractional-order systems in this paper is a systematic method. This technique is applied to achieve the lag synchronization of fractional-order Rössler's system, verified by numerical simulation.

scholarly journals Combination synchronization of fractional order n-chaotic systems using active backstepping design

2019 ◽  
Vol 8 (1) ◽  
pp. 597-608 ◽  
Author(s):  
Vijay K. Yadav ◽  
S. Das
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Design Method ◽  
Backstepping Design ◽  
Fractional Order Systems ◽  
Combination Synchronization

Abstract In this article, a scheme using active backstepping design method is proposed to achieve combination synchronization of n number of fractional order chaotic systems. In the proposed method the controllers are designed with the help of a new lemma and Lyapunov function in a systematic way. Synchronization among three/four fractional order systems have been shown as examples of synchronization of n-chaotic systems. Numerical simulation and graphical results clearly exhibit that the method of this new procedure is easy to implement and reliable for synchronization of fractional order chaotic systems.

Dynamics and Synchronization of the Fractional-Order Sprott E System

2013 ◽  
Vol 850-851 ◽  
pp. 876-879
Author(s):  
Hong Gang Dang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Attractor ◽  
Fractional Order Systems ◽  
The Stability

In this paper, dynamics and synchronization of the fractional-order Sprott E system are investigated. Firstly, the chaotic attractor of the system is got by means of numerical simulation. Then based on the stability theory of fractional-order systems, the synchronization of the system is realized. Numerical simulations are carried out to demonstrate the effectiveness of the controllers.

Synchronization of a Fractional-Order System with Unknown Parameters

2013 ◽  
Vol 850-851 ◽  
pp. 796-799
Author(s):  
Xiao Ya Yang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Attractor ◽  
Fractional Order System ◽  
Order System ◽  
Fractional Order Systems ◽  
Unknown Parameters ◽  
The Stability

In this paper, synchronization of a fractional-order system with unknown parameters is studied. The chaotic attractor of the system is got by means of numerical simulation. Then based on the stability theory of fractional-order systems, suitable synchronization controllers and parameter identification rules for the unknown parameters are designed. Numerical simulations are used to demonstrate the effectiveness of the controllers.

Adaptive Synchronization of the Fractional-Order Sprott N System

2013 ◽  
Vol 850-851 ◽  
pp. 872-875
Author(s):  
Hong Gang Dang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Phase Plane ◽  
Adaptive Synchronization ◽  
Chaotic Attractors ◽  
Fractional Order Systems ◽  
The Stability

In this paper, adaptive synchronization of the fractional-order Sprott N system is investigated. Firstly, the chaotic attractors on different phase plane of the system are got by means of numerical simulation. Then based on the stability theory of fractional-order systems, the adaptive synchronization of the system is realized. Numerical simulations are used to demonstrate the effectiveness for the controllers.

The Synchronization of Two Different Fractional-Order Systems

2014 ◽  
Vol 926-930 ◽  
pp. 3318-3321
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Attractors ◽  
Fractional Order Systems ◽  
Two Systems ◽  
The Stability

In this paper, the synchronization for two fractional-order systems is investigated. Firstly, the chaotic attractors of two systems are got by means of numerical simulation. Then based on the stability theory of fractional-order systems, the synchronization of these two systems is realized. Numerical simulations are used to demonstrate the effectiveness for the controllers.

scholarly journals A Proposed High-Gain Observer for a Class of Nonlinear Fractional-Order Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Dorsaf Etlili ◽  
Atef Khedher ◽  
Ayachi Errachdi
Keyword(s):  
Numerical Simulation ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Caputo Derivative ◽  
High Gain ◽  
Estimation Problem ◽  
Fractional Order Systems ◽  
High Gain Observer ◽  
Fractional System ◽  
Fractional Orders

This paper proposes a high-gain observer for a class of nonlinear fractional-order systems. Indeed, this approach is based on Caputo derivative to solve the estimation problem for nonlinear systems. The proposed high-gain observer is used to estimate the unknown states of a nonlinear fractional system. The use of Lyapunov convergence functions to establish stability of system is detailed. The influence of different fractional orders on the estimation is presented. Ultimately, numerical simulation examples demonstrate the efficiency of the proposed approach.

State-space analysis of linear fractional-order systems

2008 ◽  
Vol 42 (6-8) ◽  
pp. 825-838 ◽  
Author(s):  
Saïd Guermah ◽  
Saïd Djennoune ◽  
Maâmar Bettayeb
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Space Analysis ◽  
State Space Analysis
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