Passivity analysis for uncertain BAM neural networks with time delays and reaction–diffusions

Zhou, Jianping; Xu, Shengyuan; Shen, Hao; Zhang, Baoyong

doi:10.1080/00207721.2012.659693

Cited by 22 publications

(5 citation statements)

References 38 publications

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“…, n) are allowed to be positive, negative or zero. By all appearances, this hypothesis is weaker those given in [1,5,19], which require the monotonicity of the activation functions (l − i = 0) or usual Lipschitz conditions (l − i = l + i ). Such a description is precise in quantifying the lower and upper bounds of the activation functions.…”

Section: Remarkmentioning

confidence: 94%

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Synchronization for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms

Gan¹,

Liu²,

Liu³

et al. 2016

NAMC

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In this paper, the synchronization problem for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms is investigated under Dirichlet boundary conditions and Neumann boundary conditions, respectively. Based on Lyapunov stability theory, both delay-derivative-dependent and delay-range-dependent conditions are derived in terms of linear matrix inequalities (LMIs), whose solvability heavily depends on the information of reaction-diffusion terms. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. The obtained synchronization results are easy to check and improve upon the existing ones. In our results, the assumptions for the differentiability and monotonicity on the activation functions are removed. It is assumed that the state delay belongs to a given interval, which means that the lower bound of delay is not restricted to be zero. Finally, the feasibility and effectiveness of the proposed methods is shown by simulation examples.

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Section: Remarkmentioning

confidence: 94%

“…Proof. Define a Lyapunov-Krasovskii functional V (t, e(t, x)) ∈ C 2,1 (R + × R n ; R + ) for system (19) as…”

Section: Remarkmentioning

confidence: 99%

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Synchronization for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms

Gan¹,

Liu²,

Liu³

et al. 2016

NAMC

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“…30 The stabilization of reaction-diffusion systems (RDSs) has attracted wide attention as well. 9,34,35 For RDSs, there exists a specific control strategy, boundary control, to achieve FTS. 35 Boundary control only places the actuators on the boundary of the spatial region.…”

Section: Introductionmentioning

confidence: 99%

“…One mainly uses the Holder's inequality 32 while the other treats it by the generalized Gronwall's inequality 30 . The stabilization of reaction‐diffusion systems (RDSs) has attracted wide attention as well 9,34,35 . For RDSs, there exists a specific control strategy, boundary control, to achieve FTS 35 .…”

Section: Introductionmentioning

confidence: 99%

Finite‐time boundary stabilization of fractional reaction‐diffusion systems

Zhang

Wang

2022

Math Methods in App Sciences

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This paper investigates the boundary finite-time stabilization of fractional reaction-diffusion systems (FRDSs). First, a distributed controller is designed, and sufficient conditions are obtained to ensure the finite-time stability (FTS) of FRDSs under the designed controller. Then, a boundary controller is presented to achieve the FTS. By virtue of Lyapunov functional method and inequality techniques, sufficient conditions are presented to ensure the FTS of FRDSs via the designed boundary controller. The effect of diffusion term of FRDSs on the FTS is also investigated. Both Neumann and mixed boundary conditions are considered. Moreover, the robust finite-time stabilization of uncertain FRDSs is studied when there are uncertainties in the system's coefficients. Under the designed boundary controller, sufficient conditions are presented to guarantee the robust FTS of uncertain FRDSs. Finally, numerical examples are presented to verify the effectiveness of our theoretical results.

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Stability for a class of generalized reaction–diffusion uncertain stochastic neural networks with mixed delays

Gan

Xiao

2018

Int. J. Mach. Learn. & Cyber.

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Passivity analysis for uncertain BAM neural networks with time delays and reaction–diffusions

Cited by 22 publications

References 38 publications

Synchronization for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms

Synchronization for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms

Finite‐time boundary stabilization of fractional reaction‐diffusion systems

Stability for a class of generalized reaction–diffusion uncertain stochastic neural networks with mixed delays

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