SIMPLE LMI-BASED SYNCHRONIZATION OF FRACTIONAL-ORDER CHAOTIC SYSTEMS

2013 ◽  
Vol 23 (01) ◽  
pp. 1350011 ◽  
Author(s):  
SUWAT KUNTANAPREEDA
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Linear Matrix ◽  
Simple Scheme ◽  
Present Scheme ◽  
Linear Interval ◽  
Linear Interval Systems ◽  
Stabilization Theorem ◽  
Error Dynamics ◽  
Interval Systems

This paper presents a simple scheme for synchronization of fractional-order chaotic systems. The scheme utilizes a recently developed LMI (Linear matrix inequality) stabilization theorem for fractional-order linear interval systems to design a linear controller. In contrast to existing schemes in the literature, the present scheme is straightforward and does not require that nonlinear parts of synchronization error dynamics are cancelled by the controller. The fractional-order Rössler, Lorenz, and hyperchaotic Chen systems are used as demonstrative examples. Numerical results illustrate the effectiveness of the present scheme.

scholarly journals Synchronization of Uncertain Fractional-Order Hyperchaotic Systems via Unidirectional Linear Error Feedback Coupling Scheme

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Suwat Kuntanapreeda
Keyword(s):  
Fractional Order ◽  
Linear Matrix ◽  
Coupling Scheme ◽  
Simple Method ◽  
Order Linear ◽  
Synchronization Errors ◽  
Coupling Parameters ◽  
Linear Interval ◽  
Error Dynamics ◽  
Hyperchaotic Systems

A simple method for synchronization of uncertain fractional-order hyperchaotic systems is proposed in this paper. The method makes use of a unidirectional linear coupling approach due to its simple configuration and ease of implementation. To determine the coupling parameters, the synchronization error dynamics is first formulated as a fractional-order linear interval system. Then, the parameters are obtained by solving a linear matrix inequality (LMI) stability condition for stabilization of fractional-order linear interval systems. Thanks to the existence of an LMI solution, the convergence of the synchronization errors is guaranteed. The effectiveness of the proposed method is numerically illustrated by the uncertain fractional-order hyperchaotic Lorenz system.

Comments on “Takagi–Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality”

2019 ◽  
Vol 26 (9-10) ◽  
pp. 643-645
Author(s):  
Xuefeng Zhang
Keyword(s):  
Fuzzy Control ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Wide Class ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Takagi Sugeno

This article shows that sufficient conditions of Theorems 1–3 and the conclusions of Lemmas 1–2 for Takasi–Sugeno fuzzy model–based fractional order systems in the study “Takagi–Sugeno fuzzy control for a wide class of fractional order chaotic systems with uncertain parameters via linear matrix inequality” do not hold as asserted by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.

OBSERVER-BASED SYNCHRONIZATION FOR A CLASS OF FRACTIONAL CHAOTIC SYSTEMS VIA A SCALAR SIGNAL: RESULTS INVOLVING THE EXACT SOLUTION OF THE ERROR DYNAMICS

2011 ◽  
Vol 21 (03) ◽  
pp. 955-962 ◽  
Author(s):  
DONATO CAFAGNA ◽  
GIUSEPPE GRASSI
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Exact Analytical Solution ◽  
Fractional Order Systems ◽  
Fractional Error ◽  
Transmitted Signal ◽  
Error Dynamics

This paper deals with chaos synchronization for a class of fractional-order systems characterized by one nonlinearity. In particular, an observer-based approach is illustrated, which presents two remarkable features: (i) it provides an exact analytical solution of the fractional error dynamics, written in terms of Mittag-Leffler function; (ii) it enables synchronization to be achieved using a scalar transmitted signal. Finally, a synchronization example based on fractional Chua's system is illustrated, with the aim to show the capabilities of the developed approach.

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