Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks

Chen, Diyi; Zhang, Runfan; Liu, Xinzhi; Ma, Xiaoyi

doi:10.1016/j.cnsns.2014.05.005

Cited by 133 publications

(49 citation statements)

References 38 publications

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“…with matrix satisfying (12). Moreover, the stabilizing control feedback and the observer gains in (14) and (15) are given bŷ…”

Section: Theorem 13 Given Positive Scalar Design Parameter the Obsmentioning

confidence: 99%

“…Moreover, the Mittag-Leffler stability of nonlinear FOS was derived in [9,10]. In order to obtain the stability of nonlinear fractional-order time-varying systems, some authors [11,12] have proposed the extension of Lyapunov stability theorem with fractional-order to prove the stability of FOS. However, using this technique is often a really hard task, because finding a Lyapunov candidate function is more complex in the case of fractional-order.…”

Section: Introductionmentioning

confidence: 99%

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Observer-Based Robust Controller Design for Nonlinear Fractional-Order Uncertain Systems via LMI

Qiu

2017

Mathematical Problems in Engineering

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We discuss the observer-based robust controller design problem for a class of nonlinear fractional-order uncertain systems with admissible time-variant uncertainty in the case of the fractional-order satisfying 0 < < 1. Based on direct Lyapunov approach, a sufficient condition for the robust asymptotic stability of the observer-based nonlinear fractional-order uncertain systems is presented. Employing Finsler's Lemma, the systematic robust stabilization design algorithm is then proposed in terms of linear matrix inequalities (LMIs). The efficiency and advantage of the proposed algorithm are finally illustrated by two numerical simulations.

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“…with matrix satisfying (12). Moreover, the stabilizing control feedback and the observer gains in (14) and (15) are given bŷ…”

Section: Theorem 13 Given Positive Scalar Design Parameter the Obsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observer-Based Robust Controller Design for Nonlinear Fractional-Order Uncertain Systems via LMI

Qiu

2017

Mathematical Problems in Engineering

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“…Specifically, by considering the errors in (40) it can be concluded that identical synchronization (IS), antiphase synchronization (AS), and inverse full state hybrid projective synchronization (IFSHPS) coexist when synchronizing the chaotic fractional-order incommensurate Lü system (35) and the hyperchaotic fractional-order incommensurate Lorenz system (37).…”

Section: Identical Synchronization (Is) Antiphase Synchronizationmentioning

confidence: 99%

Coexistence of identical synchronization, antiphase synchronization and inverse full state hybrid projective synchronization in different dimensional fractional-order chaotic systems

et al. 2018

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The topic related to the coexistence of different synchronization types between fractional-order chaotic systems is almost unexplored in the literature. Referring to commensurate and incommensurate fractional systems, this paper presents a new approach to rigorously study the coexistence of some synchronization types between nonidentical systems characterized by different dimensions and different orders. In particular, the paper shows that identical synchronization (IS), antiphase synchronization (AS), and inverse full state hybrid projective synchronization (IFSHPS) coexist when synchronizing a three-dimensional master system with a fourth-dimensional slave system. The approach, which can be applied to a wide class of chaotic/hyperchaotic fractional-order systems in the master-slave configuration, is based on two new theorems involving the fractional Lyapunov method and stability theory of linear fractional systems. Two examples are provided to highlight the capability of the conceived method. In particular, referring to commensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Rössler system of order 2.7 and the hyperchaotic four-dimensional Chen system of order 3.84. Finally, referring to incommensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Lü system of order 2.955 and the hyperchaotic four-dimensional Lorenz system of order 3.86.

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“…Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks were discussed in [14]. In addition, the results for stability analysis and synchronization of fractional-order networks were presented in [15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

New Methods of Finite-Time Synchronization for a Class of Fractional-Order Delayed Neural Networks

Zhang

Cao

Alsaedi

et al. 2017

Mathematical Problems in Engineering

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Finite-time synchronization for a class of fractional-order delayed neural networks with fractional order , 0 < ≤ 1/2 and 1/2 < < 1, is investigated in this paper. Through the use of Hölder inequality, generalized Bernoulli inequality, and inequality skills, two sufficient conditions are considered to ensure synchronization of fractional-order delayed neural networks in a finitetime interval. Numerical example is given to verify the feasibility of the theoretical results.

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Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks

Cited by 133 publications

References 38 publications

Observer-Based Robust Controller Design for Nonlinear Fractional-Order Uncertain Systems via LMI

Observer-Based Robust Controller Design for Nonlinear Fractional-Order Uncertain Systems via LMI

Coexistence of identical synchronization, antiphase synchronization and inverse full state hybrid projective synchronization in different dimensional fractional-order chaotic systems

New Methods of Finite-Time Synchronization for a Class of Fractional-Order Delayed Neural Networks

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