Mittag-Leffler stability of fractional-order Hopfield neural networks

Zhang, Shuo; Yu, Yongguang; Hu, Wang

doi:10.1016/j.nahs.2014.10.001

Cited by 247 publications

(116 citation statements)

References 19 publications

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“…Each of the three definitions has its own properties. In this paper, we use Caputo definition because it has been extensively used in engineering applications [6,7]. The Caputo derivative of order for a function…”

Section: Preliminariesmentioning

confidence: 99%

“…Not until the last few decades had the related studies been generalized to various fields instead of pure theoretical derivation. A number of studies have revealed the potentialities of fractional calculus, such as engineering [2][3][4], physics [5], applied mathematics [6,7], and bioengineering [8]. Among these research fields, fractional-order control technology and fractional-order modeling develop quite fast.…”

Section: Introductionmentioning

confidence: 99%

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Robust Fractional‐Order PID Controller Tuning Based on Bode’s Optimal Loop Shaping

Liu

Zhang

2018

Complexity

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This paper presents a novel fractional-order PID controller tuning strategy based on Bode's optimal loop shaping which is commonly used for LTI feedback systems. Firstly, the controller parameters are achieved based on flat phase property and Bode's optimal reference model, so that the controlled system is robust to gain variations and can achieve desirable transient performance according to various control requirements. Then, robustness analysis of the controlled system is carried out to support the results. Furthermore, the parameter setting is analyzed to demonstrate the superiority of the proposed controller. At last, some simulation examples are shown to verify the accuracy and usefulness of the proposed control strategy. The proposed fractional-order PID controller does not have any restriction on the controlled plant, so it can be widely applied on both integer-order and fractionalorder systems.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Fractional‐Order PID Controller Tuning Based on Bode’s Optimal Loop Shaping

Liu

Zhang

2018

Complexity

Self Cite

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“…In [14], Zhang et al have investigated the Mittag-Leffler stability for a fractional-order neural network. In this paper, we study the Mittag-Leffler stability for a fractional-order neural network by introducing time delay term.…”

Section: Introductionmentioning

confidence: 99%

Uniform Euler approximation of solutions of fractional-order delayed cellular neural network on bounded intervals

et al. 2017

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In this paper, we study convergence characteristics of a class of continuous time fractional-order cellular neural network containing delay. Using the method of Lyapunov and Mittag-Leffler functions, we derive sufficient condition for global Mittag-Leffler stability, which further implies global asymptotic stability of the system equilibrium. Based on the theory of fractional calculus and the generalized Gronwall inequality, we approximate the solution of the corresponding neural network model using discretization method by piecewise constant argument and obtain some easily verifiable conditions, which ensures that the discrete-time analogues preserve the convergence dynamics of the continuous-time networks. In the end, we give appropriate examples to validate the proposed results, illustrating advantages of the discrete-time analogue over continuous-time neural network for numerical simulation.

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“…During the past decades, the dynamical behavior of fractional-order neural networks has attracted tremendous attention of numerous authors. For example, Wang et al [18] investigated the global stability analysis of fractional-order Hopfield neural networks with time delay, Zhang et al [22] considered the Mittag-Leffler stability of fractional-order Hopfield neural networks, Wang et al [16] discussed the asymptotic stability of delayed fractional-order neural networks with impulsive effects, Wang et al [17] focused on the stability analysis of fractional-order Hopfield neural networks with time delays. For more detailed work, we refer the readers to [5,6,8,9,14,19].…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior for fractional-order shunting inhibitory cellular neural networks

Zhao¹,

Cai²,

Fan³

2016

J. Nonlinear Sci. Appl.

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This paper deals with a class of fractional-order shunting inhibitory cellular neural networks. Applying the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique, some very verifiable criteria on the existence and uniqueness of nontrivial solution are obtained. Moreover, we also investigate the uniform stability of the fractional-order shunting inhibitory cellular neural networks. Finally, an example is given to illustrate our main theoretical findings. Our results are new and complement previously known results.

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Mittag-Leffler stability of fractional-order Hopfield neural networks

Cited by 247 publications

References 19 publications

Robust Fractional‐Order PID Controller Tuning Based on Bode’s Optimal Loop Shaping

Robust Fractional‐Order PID Controller Tuning Based on Bode’s Optimal Loop Shaping

Uniform Euler approximation of solutions of fractional-order delayed cellular neural network on bounded intervals

Dynamical behavior for fractional-order shunting inhibitory cellular neural networks

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