Robustness Analysis of Global Exponential Stability of Nonlinear Systems With Deviating Argument and Stochastic Disturbance

Zhang, Jine

doi:10.1109/access.2017.2727500

Cited by 15 publications

(24 citation statements)

References 27 publications

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“…Apparently, (2) has a zero solution, state y(t, t 0 , y 0 ) exists and is unique for any given initial values t 0 and y 0 [37]. What follows is the exponentially global stability definition of RNN (2).…”

Section: Preliminaries and Notationsmentioning

confidence: 94%

“…Remark 4. Different from the previous recurrent neural network with piecewise arguments [37], Lemma 1 has one more term than the previous lemma in [37] due to the presence of neutral terms. It is reasonable, which shows the impact of neutral terms on PRNN.…”

mentioning

confidence: 86%

“…As far as we know, some of the work is about investigating the robustness of hybrid stochastic models, nonlinear models, and recurrent models equipped with NTs without PCAs [27,28]. Some of the work has been done to explore the robustness of recurrent models with PCA subjects without NTs [14,33,36,37]. Others have also been deeply done for systems with PCAs and NTs [23,24,26], but they aim to investigate the stability instead of robustness.…”

Section: Introductionmentioning

confidence: 99%

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Exploration on Robustness of Exponentially Global Stability of Recurrent Neural Networks with Neutral Terms and Generalized Piecewise Constant Arguments

Xie

2021

Discrete Dynamics in Nature and Society

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With a view to the interference of piecewise constant arguments (PCAs) and neutral terms (NTs) to the original system and the significant applications in the signal transmission process, we explore the robustness of the exponentially global stability (EGS) of recurrent neural network (RNN) with PCAs and NTs (NPRNN). The following challenges arise: what the range of PCAs and the scope of NTs can NPRNN tolerate to be exponentially stable. So we derive two important indicators: maximum interval length of PCAs and the scope of neutral term (NT) compression coefficient here for NPRNN to be exponentially stable. Additionally, we theoretically proved that if the interval length of PCAs and the bound of NT compression coefficient are all lower than the given results herein, the disturbed NPRNN will still remain global exponential stability. Finally, there are two numerical examples to verify the deduced results’ effectiveness here.

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Section: Preliminaries and Notationsmentioning

confidence: 94%

mentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

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Exploration on Robustness of Exponentially Global Stability of Recurrent Neural Networks with Neutral Terms and Generalized Piecewise Constant Arguments

Xie

2021

Discrete Dynamics in Nature and Society

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“…Exponential stability and robustness, as for the classical dynamic behaviors of neural networks, have been studied extensively in the past few years [2,3,[13][14][15][16][17][18][19][20][21][22]. On the one hand, global exponential stability reveals the superiority that it guarantees the system can be fleetly stable at the equilibrium point with an exponential decay rate, which deservedly leads to a rapid stabilization and dramatically saves the response time.…”

Section: Introductionmentioning

confidence: 99%

Further Results on Exponentially Robust Stability of Uncertain Connection Weights of Neutral-Type Recurrent Neural Networks

Xie

2021

Complexity

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Further results on the robustness of the global exponential stability of recurrent neural network with piecewise constant arguments and neutral terms (NPRNN) subject to uncertain connection weights are presented in this paper. Estimating the upper bounds of the two categories of interference factors and establishing a measuring mechanism for uncertain dual connection weights are the core tasks and challenges. Hence, on the one hand, the new sufficient criteria for the upper bounds of neutral terms and piecewise arguments to guarantee the global exponential stability of NPRNN are provided. On the other hand, the allowed enclosed region of dual connection weights is characterized by a four-variable transcendental equation based on the preceding stable NPRNN. In this way, two interference factors and dual uncertain connection weights are mutually restricted in the model of parameter-uncertainty NPRNN, which leads to a dynamic evolution relationship. Finally, the numerical simulation comparisons with stable and unstable cases are provided to verify the effectiveness of the deduced results.

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“…Namely, differential equations with deviating argument unify delayed and advanced equations. Therefore, many open questions about systems with deviating argument are raised, some heuristic results have been shown in the relevant literature [14,15]. From another perspective, the notion of retard corresponds to the past cases, and the notion of advance corresponds to the future cases.…”

Section: Introductionmentioning

confidence: 99%

Outer-synchronization of fractional-order neural networks with deviating argument via centralized and decentralized data-sampling approaches

Cheng

Zhang

et al. 2019

Adv Differ Equ

Self Cite

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This paper is committed to investigating outer-synchronization of fractional-order neural networks with deviating argument via centralized and decentralized data-sampling approaches. Considering the low cost and high reliability of data-sampling control, we adopt two categories of control strategies with principles of centralized and decentralized data-sampling to synchronize fractional-order neural networks with deviating argument. Several sufficient criteria are proposed to realize outer-synchronization by data-sampling control design in two complex coupled networks. It is noteworthy that, based on centralized and decentralized data-sampling methods, the synchronization theory of fractional systems and differential equation with deviating argument, the sampling time points are very well selected in control systems. An example is performed to illustrate the advantage of the presented theoretical analysis and results.

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Robustness Analysis of Global Exponential Stability of Nonlinear Systems With Deviating Argument and Stochastic Disturbance

Cited by 15 publications

References 27 publications

Exploration on Robustness of Exponentially Global Stability of Recurrent Neural Networks with Neutral Terms and Generalized Piecewise Constant Arguments

Exploration on Robustness of Exponentially Global Stability of Recurrent Neural Networks with Neutral Terms and Generalized Piecewise Constant Arguments

Further Results on Exponentially Robust Stability of Uncertain Connection Weights of Neutral-Type Recurrent Neural Networks

Outer-synchronization of fractional-order neural networks with deviating argument via centralized and decentralized data-sampling approaches

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