Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays

Chen, Yonghui; Zhang, Xian; Xue, Yuncan

doi:10.1016/j.matcom.2021.10.012

Cited by 49 publications

(13 citation statements)

References 36 publications

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“…The purpose of this paper is to design a state observer (3) for DTBAMNN (1) via the measurements (2), that is, determine observer gains R := [r ij ] ∈ R n×m1 and R := [r ij ] ∈ R n×m2 guaranteeing GES of the error system (4). Lemma 1: [37] For a Metzler matrix A 0 ∈ R n×n and matrices B 0 , C 0 , D 0 ∈ R n×n , the items (a)-(c) are equivalent:…”

Section: Problem Description and Preliminary Resultsmentioning

confidence: 99%

“…The method directly uses the generalized matrix inverses and the definitions of GES, and it avoids the construction of any LKF; (2) The obtained sufficient conditions are composed of linear scalars inequalities that is easy to solve; (3) It is suitable for the more general neural network models after a small modification. For example, memristor-based NNs [40], inertial neural works [41] and high-order NNs [4], [42], [43].…”

Section: Discussionmentioning

confidence: 99%

“…Delay-dependent and -independent GES criteria, described by linear scalar inequalities, are developed by using the mathematical induction method; (2) Via generalized inverse theory of matrices, a state observer is given for DTBAMNNs with multiple time-varying delays; (3) These obtained exponential stability criteria are simple, that can easily be solved by the software YALMIP.…”

Section: Introductionmentioning

confidence: 99%

“…(i.e., Γ 1 = Γ 2 = Γ1 = Γ2 = I 2 ), then Assumption 1 is satisfied.Assume that the measurements of DTBAMNN (1) are given by(2), where M = 0.50 0.90 , M = 0.10 0.60 .Choose β = 0.02 and solve the inequalities (6) and (7) in Theorem 1 by the software YALMIP, we can get ũ = [50, 550] T , ṽ = [418.9, 600] T . ζ = [−430.3, 33.78] T , η = [−87.42, 118.73] T .…”

mentioning

confidence: 99%

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State Estimation for a Class of Discrete-Time BAM Neural Networks With Multiple Time-Varying Delays

Cong

Zhang

2023

IEEE Access

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For a class of discrete-time bidirectional associative memory neural networks (DTBAMNNs) with multiple time-varying delays, the issue of state estimation is studied. By propose a mathematical induction method, we first investigate novel delay-dependent and -independent global exponential stability (GES) criteria of the error system. The obtained GES criteria are described by linear scalar inequalities. Then, a state observer is derived via the theory of generalized matrix inverses. These exponential stability conditions are very simple, which is convenient to verify based on the standard software tools (for example, YALMIP). Finally, we present two illustrative examples to present the effectiveness of the theoretical results. INDEX TERMSState observer; Discrete-time BAM neural network; Multiple time-varying delays; Global exponential stability; Linear scalar inequalities.

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Section: Problem Description and Preliminary Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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State Estimation for a Class of Discrete-Time BAM Neural Networks With Multiple Time-Varying Delays

Cong

Zhang

2023

IEEE Access

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“…In the studies about global stability of neural networks models, discrete and continuous, it is usually assumed that the activation functions, f j , are Lipschitz [2,6,7,10,12,25,37]. Here we do not assume that f j are Lipschitz and hypothesis (H1) only implies the continuity of f j at u = 0.…”

Section: Remarkmentioning

confidence: 99%

Global exponential stability of discrete-time Hopfield neural network models with unbounded delays

Oliveira

2022

Journal of Difference Equations and Applications

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In this paper, a general setting is presented to study the exponential stability of discrete-time systems with bounded or unbounded delays. Based on the M-matrix theory, we establish sufficient conditions to ensure the global exponential stability of the zero equilibrium of low-order, and high-order, discrete-time Hopfield neural network models with unbounded delays and delay in the leakage terms. A comparison of the literature shows that our results generalize and improve some in recent publications.

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Lagrange stability of quaternion‐valued memristive neural networks

Huang,

Ma,

2024

Math Methods in App Sciences

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In this paper, the Lagrange stability (LS) for quaternion memristive neural networks with time delay is taken into consideration. On the strength of Lyapunov function, conclusions are derived such that the resultant system is stable in Lagrange sense. The analysis procedure adopts properties of quaternions instead of conventional decomposition method. The nonlinear scalarization approach is further exploited to compare the size of the quaternion, which makes the convex closures formed by quaternions more noteworthy.

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Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays

Cited by 49 publications

References 36 publications

State Estimation for a Class of Discrete-Time BAM Neural Networks With Multiple Time-Varying Delays

State Estimation for a Class of Discrete-Time BAM Neural Networks With Multiple Time-Varying Delays

Global exponential stability of discrete-time Hopfield neural network models with unbounded delays

Lagrange stability of quaternion‐valued memristive neural networks

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