Global Mittag-Leffler stability for fractional-order coupled systems on network without strong connectedness

Meng, Xin; Kao, Yonggui; Karimi, Hamid Reza; Gao, Cunchen

doi:10.1007/s11432-019-9946-6

Cited by 17 publications

(11 citation statements)

References 30 publications

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“…Some new sufficient conditions on the local SAP are derived. We will extend our results to fractional-order coupled system on a network with/without strong connectedness [36] in future.…”

Section: Resultsmentioning

confidence: 71%

Asymptotic multistability and local S-asymptotic ω-periodicity for the nonautonomous fractional-order neural networks with impulses

Kao

2020

Sci. China Inf. Sci.

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This paper focuses on the investigation of asymptotic multistability and on local S-asymptotic ω-periodicity for nonautonomous fractional-order neural networks (FONNs) with impulses. Several criteria on the existence, uniqueness, and invariant sets of nonautonomous FONNs with impulses are derived by constructing convergent sequences and comparison principles, respectively. In addition, using the Lyapunov direct method, some novel conditions of boundedness and local asymptotic stability of the FONNs discussed are obtained. Also, the sufficient conditions for local S-asymptotic ω-periodicities of the system are presented. Finally, a discussion using two examples verifies the validity of our findings, which imply that global asymptotic stability is a special case of asymptotic multistability.

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“…Some new sufficient conditions on the local SAP are derived. We will extend our results to fractional-order coupled system on a network with/without strong connectedness [36] in future.…”

Section: Resultsmentioning

confidence: 71%

Asymptotic multistability and local S-asymptotic ω-periodicity for the nonautonomous fractional-order neural networks with impulses

Kao

2020

Sci. China Inf. Sci.

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“…e external inputs u i (t) and v j (t) in system (5), which only depend on a single linear state feedback control, are designed as follows: (16).…”

Section: A Single Linear State Feedback Controlmentioning

confidence: 99%

“…Based on selected activation functions f j and g i , we have Lipschitz constants F j � G i � 1. For single state feedback controller (16), setting u 1 (t) � − 0.1x 1 (t), u 2 (t) � − 0.2x 2 (t), v 1 (t) � − 0.1y 1 (t), and v 2 (t) � − 0.2y 2 (t), we obtain a negative definite matrix H 1 :…”

Section: Numerical Simulationmentioning

confidence: 99%

“…e definitions of Mittag-Leffler stability and generalized Mittag-Leffler stability are proposed in [12,13]. Subsequently, some investigations focus on Mittag-Leffler stability [14][15][16][17][18][19][20][21]. Global Mittag-Leffler stability and synchronization analysis of discrete fractional-order complexvalued neural networks with time delay are given in [14].…”

Section: Introductionmentioning

confidence: 99%

“…In [15], the global Mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order quaternionvalued neural networks is investigated by employing the Lyapunov method. In [16], sufficient conditions ensuring the existence, uniqueness, and global Mittag-Leffler stability of the solutions of the fractional-order coupled system on a network without strong connections are derived. In [17], a new criterion is proposed to ensure the Mittag-Leffler stability for fractional-order neural networks in the quaternion field.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

Yan

Qiao

Duan

et al. 2020

Mathematical Problems in Engineering

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In this paper, the global Mittag–Leffler stabilization of fractional-order BAM neural networks is investigated. First, a new lemma is proposed by using basic inequality to broaden the selection of Lyapunov function. Second, linear state feedback control strategies are designed to induce the stability of fractional-order BAM neural networks. Third, based on constructed Lyapunov function, generalized Gronwall-like inequality, and control strategies, several sufficient conditions for the global Mittag–Leffler stabilization of fractional-order BAM neural networks are established. Finally, a numerical simulation is given to demonstrate the effectiveness of our theoretical results.

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Weight learning for ℋ∞$$ {\mathscr{H}}_{\infty } $$ stabilization of uncertain switched neural networks with external disturbance and reaction‐diffusion

Tai

Gao

Zhao

et al. 2023

Adaptive Control & Signal

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This paper considers the  ∞ stabilization of uncertain switched neural networks with external disturbance and reaction-diffusion. A weight learning rule that ensures the  ∞ stability of the network is proposed utilizing the Lyapunov-Krasovskii functional method. Then, a useful lemma concerning the equivalence of matrix inequities is derived. With the aid of the lemma and Schur complement, a more concise existence condition on the learning rule is developed. Finally, theoretical comparisons and a numerical example are given, which show that the obtained results are extensions and improvements of an existing result.

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Global Mittag-Leffler stability for fractional-order coupled systems on network without strong connectedness

Cited by 17 publications

References 30 publications

Asymptotic multistability and local S-asymptotic ω-periodicity for the nonautonomous fractional-order neural networks with impulses

Asymptotic multistability and local S-asymptotic ω-periodicity for the nonautonomous fractional-order neural networks with impulses

Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

Weight learning for ℋ∞$$ {\mathscr{H}}_{\infty } $$ stabilization of uncertain switched neural networks with external disturbance and reaction‐diffusion

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