General decay synchronization of delayed BAM neural networks via nonlinear feedback control

Sader, Malika; Abdurahman, Abdujelil; Jiang, Haijun

doi:10.1016/j.amc.2018.05.046

Cited by 23 publications

(28 citation statements)

References 29 publications

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“…Following lemma is essential to our later study, which can be proved analogously to our other work 28 and the work of Wang et al 29 Lemma 1. Under the hypothesis H 3 , assume that the solutions of e(t) and z(t) errors system (9) satisfied the differential equations .…”

Section: Preliminariesmentioning

confidence: 65%

“…If ψ ( t )= e αt and ψ ( t )=(1+ t ) α for any α >0, GDS may be specialized as exponential synchronization and polynomial synchronization. H 3 : For the functions

ψ false(t false), \overset{ψ}{true} false(t false)

given in Definition , there exist a positive function ϱ ( t )∈ C ( R , R + ) and a real number θ such that

\tilde{ψ} (t) \leq 1, \sup_{t \in [0, + \infty)} \int_{0}^{t} ψ^{θ} (s) ϱ (s) d s < + \infty, for any t \geq 0 .

Following lemma is essential to our later study, which can be proved analogously to our other work and the work of Wang et al…”

Section: Preliminariesmentioning

confidence: 69%

“…Remark For the synchronization conditions given in other works, the time delays assumed to be constant delays or time‐varying delays that are differentiable such that their derivatives are not greater than one. Note that, in our assumption H 1 , those restrictions are removed in this paper, which means that our established results have a wider applicability.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…The time evolution of synchronization errors between master-slave systems (38) and (39) are shown in Figures 7, 8, and 9, where the initial values of slave Remark 8. For the synchronization conditions given in other works, 2,23,24,[27][28][29][30]39 the time delays assumed to be constant delays or time-varying delays that are differentiable such that their derivatives are not greater than one. Note that, in our assumption H 1 , those restrictions are removed in this paper, which means that our established results have a wider applicability.…”

Section: Examplementioning

confidence: 99%

“…Therefore, realizing synchronization between master‐salve chaotic systems via introducing an output feedback controller is more desirable and indeed very important in both theory and applications, which is yet a quite challenging problem . On the other hand, as mentioned in other works, it is a very interesting problem to find estimate of the convergent rate of solution for nonlinear systems. However, in some special cases, the convergence rate of the synchronization cannot be shown or it is not easy to estimate .…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear output control scheme for general decay synchronization of delayed neural networks with inertial term

Abdurahman

Jiang

Sader

2019

Intl J Robust & Nonlinear

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Summary This study is mainly concerned with the general decay synchronization (GDS) problem of a class of inertial neural networks (INNs) with time‐varying delay. First, unlike the methods used in previous relevant literature where both of the master and slave systems were transferred into the first‐order differential equations, only error dynamical system is transferred into the reduced‐order differential equation. Then, by designing a novel nonlinear output feedback controller and constructing suitable Lyapunov functionals, some simple and useful sufficient conditions ensuring the GDS of considered INNs are established via employing useful analysis techniques and linear matrix inequality approach. In addition, two examples are presented to show the effectiveness of the established theoretical results.

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Section: Preliminariesmentioning

confidence: 65%

“…If ψ ( t )= e αt and ψ ( t )=(1+ t ) α for any α >0, GDS may be specialized as exponential synchronization and polynomial synchronization. H 3 : For the functions

ψ false(t false), \overset{ψ}{true} false(t false)

given in Definition , there exist a positive function ϱ ( t )∈ C ( R , R + ) and a real number θ such that

\tilde{ψ} (t) \leq 1, \sup_{t \in [0, + \infty)} \int_{0}^{t} ψ^{θ} (s) ϱ (s) d s < + \infty, for any t \geq 0 .

Following lemma is essential to our later study, which can be proved analogously to our other work and the work of Wang et al…”

Section: Preliminariesmentioning

confidence: 69%

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear output control scheme for general decay synchronization of delayed neural networks with inertial term

Abdurahman

Jiang

Sader

2019

Intl J Robust & Nonlinear

Self Cite

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Exponential stability of positive neural networks in bidirectional associative memory model with delays

Hien

Hai-An

2019

Math Methods in App Sciences

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This paper is concerned with the problem of exponential stability of positive neural networks in bidirectional associative memory (BAM) model with multiple time-varying delays and nonlinear self-excitation rates. On the basis of a systematic approach involving extended comparison techniques via differential inequalities, we first prove the positivity of state trajectories initializing from a positive cone called the admissible set of initial conditions. In combination with the use of Brouwer's fixed point theorem and M-matrix theory, we then derive conditions for the existence and global exponential stability of a unique positive equilibrium of the model. An extension to the case of BAM neural networks with proportional delays is also presented. The effectiveness of the obtained results is illustrated by a numerical example with simulations. KEYWORDS exponential stability, M-matrix, positve BAM neural networks, time-varying delays MSC CLASSIFICATION 34 K20; 34 K45; 92C42

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Delay‐dependent criteria for general decay synchronization of discontinuous fuzzy neutral‐type neural networks with time‐varying delays

Kong

Sakthivel

2020

Intl J Robust & Nonlinear

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This paper aims to investigate the general decay synchronization analysis of discontinuous fuzzy neutral-type neural networks. Under the framework of Filippov solutions, based on functional differential inclusions theory, inequality technique and by constructing a modified delay-dependent Lyapunov-Krasovskii functional, some new delay-dependent criteria are provided to guarantee the general decay synchronization via the effective nonlinear feedback controller. The neural network model considered is more generalized, some previous fuzzy neural networks can be regard as the special cases. Moreover, some recent results on the delay-independent criteria ensuring the general decay synchronization can also be extended and concluded. These can be seen from the given corollaries and remarks which are provided to make the comparisons and show the advantages. Finally, some numerical examples and simulations are provided to illustrate the correctness.

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General decay synchronization of delayed BAM neural networks via nonlinear feedback control

Cited by 23 publications

References 29 publications

Nonlinear output control scheme for general decay synchronization of delayed neural networks with inertial term

Nonlinear output control scheme for general decay synchronization of delayed neural networks with inertial term

Exponential stability of positive neural networks in bidirectional associative memory model with delays

Delay‐dependent criteria for general decay synchronization of discontinuous fuzzy neutral‐type neural networks with time‐varying delays

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