scholarly journals Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Cuimei Jiang ◽  
Akbar Zada ◽  
M. Tamer Şenel ◽  
Tongxing Li
Keyword(s):  
Fractional Order ◽  
Lyapunov Functions ◽  
Chaotic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Order Error ◽  
Synchronization Problem ◽  
Direct Design ◽  
Error System ◽  
Theoretical Results

Abstract This paper discusses the synchronization problem of N-coupled fractional-order chaotic systems with ring connection via bidirectional coupling. On the basis of the direct design method, we design the appropriate controllers to transform the fractional-order error dynamical system into a nonlinear system with antisymmetric structure. By choosing appropriate fractional-order Lyapunov functions and employing the fractional-order Lyapunov-based stability theory, several sufficient conditions are obtained to ensure the asymptotical stabilization of the fractional-order error system at the origin. The proposed method is universal, simple, and theoretically rigorous. Finally, some numerical examples are presented to illustrate the validity of theoretical results.

scholarly journals Robust Synchronization Controller Design for a Class of Uncertain Fractional Order Chaotic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Lin Wang ◽  
Chunzhi Yang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Closed Loop System ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Lyapunov Stability Criterion ◽  
Theoretical Results

Synchronization problem for a class of uncertain fractional order chaotic systems is studied. Some fundamental lemmas are given to show the boundedness of a complicated infinite series which is produced by differentiating a quadratic Lyapunov function with fractional order. By using the fractional order extension of the Lyapunov stability criterion and the proposed lemma, stability of the closed-loop system is analyzed, and two sufficient conditions, which can enable the synchronization error to converge to zero asymptotically, are driven. Finally, an illustrative example is presented to confirm the proposed theoretical results.

scholarly journals Synchronization of Coupled Chaotic Systems with Ring Connection Based on Special Antisymmetric Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiangyong Chen ◽  
Jianlong Qiu ◽  
Qiang Song ◽  
Ancai Zhang
Keyword(s):  
Theoretical Analysis ◽  
Chaotic Systems ◽  
Design Method ◽  
Stable System ◽  
Stability Criteria ◽  
Complete Synchronization ◽  
Numerical Examples ◽  
Synchronization Problem ◽  
Direct Design ◽  
Error System

This paper considers the complete synchronization problem for coupled chaotic systems with ring connections. First, we use a direct design method to design a synchronization controller. It transforms the error system into a stable system with special antisymmetric structure. And then, we get some simple stability criteria of achieving the complete synchronization. These criteria are not only easily verified but also improve and generalize previous known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical analysis.

scholarly journals Generalized Synchronization of Different Chaotic Systems Based on Nonnegative Off-Diagonal Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Ling Guo ◽  
Xiaohong Nian ◽  
Huan Pan
Keyword(s):  
Chaotic Systems ◽  
Matrix Theory ◽  
Design Method ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Generalized Synchronization ◽  
Synchronization Problem ◽  
Direct Design ◽  
The Stability ◽  
Different Chaotic Systems

The generalized synchronization problem is studied in this paper for different chaotic systems with the aid of the direct design method. Based on Lyapunov stability theory and matrix theory, some sufficient conditions guaranteeing the stability of a nonlinear system with nonnegative off-diagonal structure are obtained. Then the control scheme is designed from the stable system by the direct design method. Finally, two numerical simulations are provided to verify the effectiveness and feasibility of the proposed method.

Hybrid Synchronization of Three Identical Coupled Chaotic Systems Using the Direct Design Method

2014 ◽  
Vol 912-914 ◽  
pp. 695-699 ◽  
Author(s):  
Xiu Huan Ji
Keyword(s):  
Nonlinear System ◽  
Theoretical Analysis ◽  
Stability Criterion ◽  
Chaotic Systems ◽  
Design Method ◽  
Complete Synchronization ◽  
Numerical Example ◽  
Direct Design ◽  
Error System ◽  
Hybrid Synchronization

This paper investigates the hybrid synchronization behavior (coexistence of anti-synchronization and complete synchronization) in three coupled chaotic systems with ring connections. We employ the direct design method to design the hybird synchronization controllers, which transform the error system into a nonlinear system with a special antisymmetric structure. A simple stability criterion is then derived for reaching hybrid synchronization. Finally, numerical example is provided to demonstrate the effectiveness of the theoretical analysis.

scholarly journals Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 473 ◽  
Author(s):  
Ravi Agarwal ◽  
Snezhana Hristova ◽  
Donal O’Regan
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Lyapunov Functions ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Output Coupling ◽  
Synchronization Problem ◽  
Caputo Fractional Differential Equations ◽  
Derivatives Of

The synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly on the moments of impulses and we consider both the cases of state coupling controllers and output coupling controllers. The fractional generalization of the Razumikhin method and Lyapunov functions is applied. Initially, a brief overview of the basic fractional derivatives of Lyapunov functions used in the literature is given. Some sufficient conditions are derived to realize the global Mittag–Leffler synchronization of impulsive fractional-order neural networks. Our results are illustrated with examples.

Synchronization and anti-synchronization of N different coupled chaotic systems with ring connection

2014 ◽  
Vol 25 (05) ◽  
pp. 1440011 ◽  
Author(s):  
Xiangyong Chen ◽  
Chengyong Wang ◽  
Jianlong Qiu
Keyword(s):  
Chaotic Systems ◽  
Design Method ◽  
Stable System ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Synchronization Problem ◽  
Symmetric Structure ◽  
Direct Design

This paper considers the synchronization and anti-synchronization problem of N different coupled chaotic systems with ring connections. Employing the direct design method to design the synchronization and anti-synchronization controllers which can transform the error systems into a stable system with special anti-symmetric structure. Some simple stability criteria are then derived for reaching the synchronization in such systems. It is proved that these criteria not only are easily verified, but also improve and generalize previously known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical.

scholarly journals Design of unknown input fractional-order observers for fractional-order systems

2013 ◽  
Vol 23 (3) ◽  
pp. 491-500 ◽  
Author(s):  
Ibrahima N’Doye ◽  
Mohamed Darouach ◽  
Holger Voos ◽  
Michel Zasadzinski
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Order Error ◽  
Error System ◽  
Time Linear

Abstract This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1≤α<2 and 0<α≤1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.

Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness

2021 ◽  
pp. 014233122110009
Author(s):  
Xin Meng ◽  
Baoping Jiang ◽  
Cunchen Gao
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Coupled Systems ◽  
Projective Synchronization ◽  
Slave System ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Strong Connectedness ◽  
Master System ◽  
Error System

This paper considers the Mittag-Leffler projective synchronization problem of fractional-order coupled systems (FOCS) on the complex networks without strong connectedness by fractional sliding mode control (SMC). Combining the hierarchical algorithm with the graph theory, a new SMC strategy is designed to realize the projective synchronization between the master system and the slave system, which covers the globally complete synchronization and the globally anti-synchronization. In addition, some novel criteria are derived to guarantee the Mittag-Leffler stability of the projective synchronization error system. Finally, a numerical example is given to illustrate the validity of the proposed method.

Complex projection synchronization of fractional order uncertain complex-valued networks with time-varying coupling

2019 ◽  
Vol 33 (29) ◽  
pp. 1950351 ◽  
Author(s):  
Dawei Ding ◽  
Xiaolei Yao ◽  
Hongwei Zhang
Keyword(s):  
Fractional Order ◽  
Coupling Strength ◽  
Dynamic Networks ◽  
Sufficient Conditions ◽  
Feedback Gain ◽  
Time Varying ◽  
Order Complex ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Complex Valued

In this paper, the complex projection synchronization problem of fractional complex-valued dynamic networks is investigated. Considering the time-varying coupling and unknown parameters of the fractional order complex network, several decentralized adaptive strategies are designed to adjust the coupling strength and controller feedback gain in order to investigate the complex projection synchronization problem of the system. Moreover, based on the designed identification law, the uncertain parameters in the network can be estimated. Using adaptive law which balances the time-varying coupling strength and the feedback gain of the controller, some sufficient conditions are obtained for the complex projection synchronization of complex networks. Finally, numerical simulation examples are provided to illustrate the efficiency of the complex projection synchronization strategies of the fractional order complex dynamic networks.

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.

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