Synchronization of switched neural networks with mixed delays via impulsive control

Yang, Xinsong; Huang, Chuangxia; Zhu, Quanxin

doi:10.1016/j.chaos.2011.06.006

Cited by 72 publications

(47 citation statements)

References 39 publications

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“…On the other hand, because of switching phenomenon, frequency change, or other sudden noise, the states of nodes in many real-world dynamical networks are often subject to instantaneous perturbations and experience abrupt changes at certain instants, i.e., they exhibit impulsive effects [31][32][33][34][35][36][37][38][41][42][43][44]. Impulsive effects can also be found in many evolutionary processes and biological systems [31,32,41].…”

Section: Introductionmentioning

confidence: 99%

Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks: average impulsive interval approach

Cai

Jia

et al. 2016

Nonlinear Dyn

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In this paper, the problem of exponential cluster synchronization of general hybrid-coupled impulsive dynamical networks with internal delay and delayed coupling is investigated. A more general delayed coupling term including different transmission delay and self-feedback delay is taken into account. By using average impulsive interval approach and the analysis technique, some novel globally exponential cluster synchronization criteria are derived analytically. It is noted that the internal delay, transmission delay and self-feedback delay are all time-varying and can be different from each other, the inner connecting matrices are not demanded to be diagonal and the coupling matrices are not restricted to be symmetric or irreducible, more consistent with the realistic networks. Particularly, it is shown that the derived cluster synchronization criteria are simultaneously applicable for studying general delayed dynamical networks with

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Section: Introductionmentioning

confidence: 99%

Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks: average impulsive interval approach

Cai

Jia

et al. 2016

Nonlinear Dyn

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“…Letting ! 0, one gets from the lemma 3 in Yang et al (2011a) (1) and (16) can achieve global exponential synchronization under the impulsive controller (31), if the inequalities (33), (34) and the following inequality hold:…”

Section: Under the Impulsive Controller (32)mentioning

confidence: 99%

“…Lemma 5 Yang et al (2011a). Suppose KðtÞ is a nonnegative bounded scalar function defined on ½0; þ1Þ and…”

Section: Definitionmentioning

confidence: 99%

“…The application of distributed delay can be found in Tank and Hopfield (1987), where a neural circuit with bounded distributed delays has been designed to solve a general problem of recognizing patterns in a time-dependent signal. Although there were many results on synchronization of continuous neural networks with discrete and distributed delays (mixed delays) (Cao et al 2007;Wang et al 2010;Yang et al 2011a), as far as we know, result on synchronization of neural networks with discontinuous activations and mixed delays is few.…”

Section: Introductionmentioning

confidence: 99%

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Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control

Yang

Cao

2014

Cogn Neurodyn

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This paper investigates drive-response synchronization for a class of neural networks with timevarying discrete and distributed delays (mixed delays) as well as discontinuous activations. Strict mathematical proof shows the global existence of Filippov solutions to neural networks with discontinuous activation functions and the mixed delays. State feedback controller and impulsive controller are designed respectively to guarantee global exponential synchronization of the neural networks. By using Lyapunov function and new analysis techniques, several new synchronization criteria are obtained. Moreover, lower bound on the convergence rate is explicitly estimated when state feedback controller is utilized. Results of this paper are new and some existing ones are extended and improved. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.

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“…For instance, divergent trajectories can be generated by switching appropriately among stable subsystems, while a proper switching signal may ensure stability of a switched system even when all the subsystems are unstable. Due to such interesting features, stability of switched systems has attracted considerable research attention over the past few decades; see [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Input‐to‐State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

Peng

Cao

2018

Complexity

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This paper studies the input-to-state stability (ISS) of nonlinear switched systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained. In our approach, the timederivative of the Lyapunov function is not necessarily negative definite and that allows wider applications than existing results in the literature. Examples are provided to illustrate the applications and advantages of our general results and the proposed approach.

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Synchronization of switched neural networks with mixed delays via impulsive control

Cited by 72 publications

References 39 publications

Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks: average impulsive interval approach

Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks: average impulsive interval approach

Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control

Input‐to‐State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

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