Synchronization in time-discrete delayed chaotic systems

Su, Huan; Ding, Xiaohua

doi:10.1016/j.neucom.2009.06.014

Cited by 11 publications

(2 citation statements)

References 21 publications

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“…Inspired by the standard neural network model in [20]- [22], a unified model which consists of a linear dynamic system and a static nonlinear operator is adopted to describe the discrete-time systems such as recurrent multilayer perceptrons (RMLPs) [2], complex systems [12], Hopfield neural network [23]- [24], Chua's circuits [25], Duffing Holmes chaotic system [26]- [27], etc. Based on this model, we concentrate on the H ∞ synchronization controller design issue for discrete-time nonlinear systems with interval timevarying delays.…”

Section: Introductionmentioning

confidence: 99%

H<inf>∞</inf> synchronization for a class of discrete-time nonlinear systems with interval time-varying delays

Chen

Liu

Fan

et al. 2014

Proceedings of the 33rd Chinese Control Conference

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This paper investigates the H∞ synchronization problem for two discrete time-varying-delayed nonlinear systems such as Hopfield neural networks, complex systems, recurrent multilayer perceptrons (RMLPs), Chua's circuits etc., which can be transformed into the unified model consisting of a linear dynamic system and a static nonlinear operator. Throughout the paper, first a response system is established according to the drive-response concept. Second, the H∞ performance for the synchronization error dynamical system between the drive model and the response model is analyzed based on the Lyapunov stability theory and linear matrix inequality (LMI) technique. Then, based on the analysis, a state feedback controller is designed to guarantee the H∞ performance for the synchronization error dynamical system. During the design procedure, novel Lyapunov functions are established to increase the upper bounds of the time-varying delays with their lower bounds fixed such that the conservatism of conditions for the feedback controller synthesis is reduced. Finally an illustrative example is provided to verify the effectiveness of the proposed control laws.

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Section: Introductionmentioning

confidence: 99%

H<inf>∞</inf> synchronization for a class of discrete-time nonlinear systems with interval time-varying delays

Chen

Liu

Fan

et al. 2014

Proceedings of the 33rd Chinese Control Conference

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show abstract

“…In [18], the controlled synchronization problem for a class of nonlinear discrete-time chaotic systems subjected to limited communication capacity has been introduced by Liu et al A fuzzy model-based adaptive approach to synchronize two different discrete-time chaotic systems with unknown parameters is presented by Vasegh and Majd [19]. Su and Ding [20] have used the Euler method to a discrete delayed chaotic system and achieved the globally exponential synchronization under the negative feedback control. There have already been a lot of research results about synchronization of the discrete-time chaotic systems [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Generalized Synchronization of Stochastic Discrete Chaotic System with Poisson Distribution Coefficient

Ma¹,

Dong²,

Zheng³

2013

Discrete Dynamics in Nature and Society

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This paper addresses the generalized synchronization of stochastic discrete chaotic systems with Poisson distribution coefficient. Firstly, based on the orthogonal polynomial approximation theory of discrete random function in Hilbert spaces, the discrete chaotic system with random parameter is transformed into its equivalent deterministic system. Secondly, a general method for the generalized synchronization of discrete chaotic system with random parameter is presented by Lyapunov stability theory and contraction theorem. Finally, two synchronization examples numerically illustrated that the proposed control scheme is effective for any stochastic discrete system.

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Adaptive synchronization of stochastic neural networks with mixed time delays and reaction–diffusion terms

Gan¹

2012

Nonlinear Dyn

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Synchronization in time-discrete delayed chaotic systems

Cited by 11 publications

References 21 publications

H<inf>∞</inf> synchronization for a class of discrete-time nonlinear systems with interval time-varying delays

H<inf>∞</inf> synchronization for a class of discrete-time nonlinear systems with interval time-varying delays

Generalized Synchronization of Stochastic Discrete Chaotic System with Poisson Distribution Coefficient

Adaptive synchronization of stochastic neural networks with mixed time delays and reaction–diffusion terms

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Synchronization in time-discrete delayed chaotic systems

Cited by 11 publications

References 21 publications

H<inf>&#x221E;</inf> synchronization for a class of discrete-time nonlinear systems with interval time-varying delays

H<inf>&#x221E;</inf> synchronization for a class of discrete-time nonlinear systems with interval time-varying delays

Generalized Synchronization of Stochastic Discrete Chaotic System with Poisson Distribution Coefficient

Adaptive synchronization of stochastic neural networks with mixed time delays and reaction–diffusion terms

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H<inf>∞</inf> synchronization for a class of discrete-time nonlinear systems with interval time-varying delays

H<inf>∞</inf> synchronization for a class of discrete-time nonlinear systems with interval time-varying delays