Nonfragile stabilization for uncertain system with interval time‐varying delays via a new double integral inequality

Samidurai, Rajendran; Sriraman, Ramalingam; Cao, Jinde; Tu, Zhengwen

doi:10.1002/mma.5137

Cited by 14 publications

(8 citation statements)

References 53 publications

(147 reference statements)

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“…Proof We divide the proof into three steps for convenience. The main aim of step 1 is to show the stability of system (3). The moment estimation on E|x(t)y(t)| p has been performed in step 2.…”

Section: Theorem 31 Let Assumption 1 and 2λ + (-mentioning

confidence: 99%

“…Step 2. The main aim now is to estimate the pth moment for solution process x(t) and the difference process x(t)y(t) between networks (2) and (3). Applying Itô's formula to |x(t)| 2 yields…”

Section: Theorem 31 Let Assumption 1 and 2λ + (-mentioning

confidence: 99%

“…Next we estimate the pth moment difference between networks (2) and (3). By Itô's formula and the Hölder inequality, we get…”

Section: Theorem 31 Let Assumption 1 and 2λ + (-mentioning

confidence: 99%

“…(2) By the stochastic comparison principle and Itô's formula, the stochastic intermittent stabilization based on delay feedback control can be obtained. (3) We succeed in overcoming the difficulties mainly arising from the simultaneous presence of the intermittent noise and delay feedback control.…”

Section: Introductionmentioning

confidence: 98%

“…Nowadays they are widely applied in several areas, such as imagine processing, communication engineering, and optimization. These applications mainly depend on the asymptotic behavior of the neural networks [1][2][3][4][5], especially their stability, and therefore more and more authors study the stability of neural networks. The readers can refer to [6][7][8][9][10] and their references.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Almost sure exponential stabilization of neural networks by aperiodically intermittent control based on delay observations

Liu

Feng

2019

Adv Differ Equ

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This paper is concerned with almost sure exponential stabilization of neural networks by intermittent control based on delay observations. By the stochastic comparison principle and Itô's formula, a sufficient criterion is derived, under which unstable neural networks can be stabilized by stochastic intermittent control based on delay observations. The range of intermittent rate is given, and the upper bound of time delay can be solved from a transcend equation. Finally, two examples are provided to demonstrate the feasibility and validity of our proposed methods.

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Section: Theorem 31 Let Assumption 1 and 2λ + (-mentioning

confidence: 99%

Section: Theorem 31 Let Assumption 1 and 2λ + (-mentioning

confidence: 99%

“…Next we estimate the pth moment difference between networks (2) and (3). By Itô's formula and the Hölder inequality, we get…”

Section: Theorem 31 Let Assumption 1 and 2λ + (-mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Almost sure exponential stabilization of neural networks by aperiodically intermittent control based on delay observations

Liu

Feng

2019

Adv Differ Equ

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Synchronization control of quaternion‐valued inertial memristor‐based neural networks via adaptive method

Zhang,

Wei,

Cao

et al. 2023

Math Methods in App Sciences

Self Cite

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In this paper, by introducing memristive connections and inertial term into quaternion‐valued neural networks, the quaternion‐valued inertial memristive neural networks (QVIMNNs) is proposed. Based on the adaptive control strategy, the synchronization problem of the QVIMNNs is analyzed in this work. Two different assumption for activation functions are considered in this work; new criteria for global synchronization are then derived by designing novel adaptive controllers and update laws. Lastly, numerical examples are given to verify the results obtained in this work.

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State estimation and structure identification of complex networks with time‐varying delays and model uncertainty based on probabilistic graph neural network

Ma,

Wang

2024

Intl J Robust & Nonlinear

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SummaryIn this paper, the state estimation problem and structure identification problem are investigated for an array of complex networks with time‐varying delays and model uncertainty. Model uncertainty is generated by uncertain connections between nodes in complex networks. Combining probabilistic graph model and graph neural network, a probabilistic graph neural network is proposed to deal with the uncertainty, and the multiple linear terms of the errors between nodes are estimated. The purpose of the addressed state estimation problem is to design a state estimator such that, in the presence of the model uncertainty, the estimation error to converge to zero can be guaranteed and the explicit expression of the estimator parameters is given. Based on a Lyapunov function, the parameters of the estimator and the updating laws of the weights of probabilistic graph neural network can be obtained by the solutions to linear matrix inequalities. The purpose of the addressed structure identification problem is to infer a definite graph structure model based on Bayes' theorem in the presence of a stable probabilistic graph neural network and state estimator. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation and structure identification scheme.

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Nonfragile stabilization for uncertain system with interval time‐varying delays via a new double integral inequality

Cited by 14 publications

References 53 publications

Almost sure exponential stabilization of neural networks by aperiodically intermittent control based on delay observations

Almost sure exponential stabilization of neural networks by aperiodically intermittent control based on delay observations

Synchronization control of quaternion‐valued inertial memristor‐based neural networks via adaptive method

State estimation and structure identification of complex networks with time‐varying delays and model uncertainty based on probabilistic graph neural network

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