Impulsive Control Via Variable Impulsive Perturbations on a Generalized Robust Stability for Cohen–Grossberg Neural Networks With Mixed Delays

Cao, Jinde; Stamov, Trayan; Sotirov, Sotir; Sotirova, Evdokia; Stamova, Ivanka

doi:10.1109/access.2020.3044191

Cited by 10 publications

(4 citation statements)

References 65 publications

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“…In Zhou et al [9], the intensity for Poisson distribution ℵ = 1.5, while we need ℵ = 0.2 in Example 4.1 and ℵ = 0.8 in Example 4.2. In the paper [9], if we choose smaller intensity for Poisson distribution such as ℵ = 1, the stability condition (17) in that article does not hold, which means that the system may not be stable. Secondly, compared with reference The method in paper by Li and Deng [8] 0.8956 0.9937 [8], the stability conditions value we obtained are broader.…”

Section: Numerical Examplementioning

confidence: 99%

“…The Cohen-Grossberg neural networks (CGNNs) molding is a special type of NNs which was originally raised and researched by Cohen Grossberg in 1983 [16]. Over the past few decades, its utilization in classification, signal, sophisticated optimization problem, and concurrent computation has been extensively studied [17][18][19]. As far as we know, there have been more and more investigations on the stability of CGNNs in recent years, such as p-th moment stability [20,21], globally exponential stability [22], robust exponential stability [23,24], and almost sure stability [25,26].…”

Section: Introductionmentioning

confidence: 99%

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Almost sure stability of stochastic neutral Cohen–Grossberg neural networks with Lévy noise and time‐varying delays

Deng

2022

Asian Journal of Control

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The almost sure stability for the stochastic neutral Cohen–Grossberg neural networks (SNCGNNs) with Lévy noise, time‐varying delays, and Markovian switching would be deliberated in this article. By means of the nonnegative semimartingale convergence theorem (NSCT), the neutral Itô formula, M‐matrix method, and selecting appropriate Lyapunov function, several almost sure stability criterions for the SNCGNNs could be derived. Moreover, according to the M‐matrix theory, the upper bounds of the coefficients at any mode are given. Finally, two examples and numerical simulations verify the correctness of theoretical analysis for the stability criterions proposed in the article.

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Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Almost sure stability of stochastic neutral Cohen–Grossberg neural networks with Lévy noise and time‐varying delays

Deng

2022

Asian Journal of Control

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“…Impulsive control has wide applications in real world. Some useful impulsive control approaches have been presented in many fields such as in financial models, epidemic models, neural networks and so on [6,7,17,19,21,25]. As is known to us, impulsive control is a discontinuous control.…”

Section: Introductionmentioning

confidence: 99%

Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

You

Sun

2022

NAMC

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This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our results

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“…For robust stability analysis, researchers have actively developed efficient robust design methods in order to reduce the unstable and/or inconsistent data results arising from the uncertainties and achieve an optimal design. Among all methods, the Lyapunov function method has been successfully applied to investigate the robustness in a variety of models with uncertain terms [43][44][45][46][47], including models in engineering such as robotic manipulators [48,49], high speed rotors [50], aircraft and aerospace systems [51,52]. In [53] the Lyapunov-based approach is applied in the lithium-ion batteries accurate state estimation in order to maintain accuracy and robustness.…”

Section: Introductionmentioning

confidence: 99%

Neural Networks in Engineering Design: Robust Practical Stability Analysis

Stamov

2021

Cybernetics and Information Technologies

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In recent years, we are witnessing artificial intelligence being deployed on embedded platforms in our everyday life, including engineering design practice problems starting from early stage design ideas to the final decision. One of the most challenging problems is related to the design and implementation of neural networks in engineering design tasks. The successful design and practical applications of neural network models depend on their qualitative properties. Elaborating efficient stability is known to be of a high importance. Also, different stability notions are applied for differently behaving models. In addition, uncertainties are ubiquitous in neural network systems, and may result in performance degradation, hazards or system damage. Driven by practical needs and theoretical challenges, the rigorous handling of uncertainties in the neural network design stage is an essential research topic. In this research, the concept of robust practical stability is introduced for generalized discrete neural network models under uncertainties applied in engineering design. A robust practical stability analysis is offered using the Lyapunov function method. Since practical stability concept is more appropriate for engineering applications, the obtained results can be of a practical significance to numerous engineering design problems of diverse interest.

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Impulsive Control Via Variable Impulsive Perturbations on a Generalized Robust Stability for Cohen–Grossberg Neural Networks With Mixed Delays

Cited by 10 publications

References 65 publications

Almost sure stability of stochastic neutral Cohen–Grossberg neural networks with Lévy noise and time‐varying delays

Almost sure stability of stochastic neutral Cohen–Grossberg neural networks with Lévy noise and time‐varying delays

Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

Neural Networks in Engineering Design: Robust Practical Stability Analysis

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