Exponential stability of Markovian jumping Cohen–Grossberg neural networks with mixed mode-dependent time-delays

Liu, Yurong; Liu, Weibo; Obaid, Mustafa A. A.; Abbas, Ibrahim A.

doi:10.1016/j.neucom.2015.11.046

Cited by 144 publications

(36 citation statements)

References 37 publications

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“…Now, the first part that appeared in system (7) has been well considered, for the second part, one has:…”

Section: Main Results and Proofsmentioning

confidence: 99%

“…Recently, neural networks, including the Hopfield neural networks, the Cohen‐Grossberg (C‐G) neural networks, and the cellular neural networks, have been extensively investigated and many interesting results have been obtained. () Among which, the stability analysis of the C‐G system with stochastic and reaction‐diffusion terms is considered in Shi and Zhu, whereas Liu et al paid attention to the C‐G system with Markovian jumping() and investigated the C‐G neural networks with complex‐valued parameters. However, there are no publishing results concentrated on the C‐G neural networks with quaternions parameters so far, which constituted one of the motives of this paper.…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis of quaternion‐valued Cohen‐Grossberg neural networks

Gao

Cao

et al. 2019

Math Methods in App Sciences

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In this paper, by starting from basic quaternion algebra properties and algorithms, a quaternion‐valued Cohen‐Grossberg neural network was derived, subsequently, several new sufficient conditions are derived to ensure existence and global asymptotic stability (GAS) and global exponential stability (GES) of the equilibrium point (EP) for quaternion‐valued Cohen‐Grossberg neural networks. The obtained criteria can be checked easily in practice and have a distinguished feature from previous studies. Finally, we have numerical evidences that the mathematical system and the conclusions presented are validated.

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“…Now, the first part that appeared in system (7) has been well considered, for the second part, one has:…”

Section: Main Results and Proofsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability analysis of quaternion‐valued Cohen‐Grossberg neural networks

Gao

Cao

et al. 2019

Math Methods in App Sciences

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“…Finally, numerical simulations have been given to illustrate the applicability and usefulness of the developed theoretical results. It is worth mentioning that the proposed method in this paper can be extended to address the nonfragile state estimation problems for Markovian jump systems as in [40,41] with different types of time delays and time-varying systems in [42][43][44] with unreliable measurements, which constitute interesting topic for future research. …”

Section: Resultsmentioning

confidence: 99%

Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

2017

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We deal with the design problem of nonfragile state estimator for discrete-time genetic regulatory networks (GRNs) with timevarying delays and randomly occurring uncertainties. In particular, the norm-bounded uncertainties enter into the GRNs in random ways in order to reflect the characteristic of the modelling errors, and the so-called randomly occurring uncertainties are characterized by certain mutually independent random variables obeying the Bernoulli distribution. The focus of the paper is on developing a new nonfragile state estimation method to estimate the concentrations of the mRNA and the protein for considered uncertain delayed GRNs, where the randomly occurring estimator gain perturbations are allowed. By constructing a LyapunovKrasovskii functional, a delay-dependent criterion is obtained in terms of linear matrix inequalities (LMIs) by properly using the discrete-time Wirtinger-based inequality and reciprocally convex combination approach as well as the free-weighting matrix method. It is shown that the proposed method ensures that the estimation error dynamics is globally asymptotically stable and the desired estimator parameter is designed via the solutions to certain LMIs. Finally, we provide two numerical examples to illustrate the feasibility and validity of the proposed estimation results.

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“…Therefore, it is of great importance to consider the random effect on the stability of neural frameworks with parameter uncertainties [39][40][41]. On the other hand, Markovian jump neural networks can be regarded as a special class of hybrid systems, which 2 Mathematical Problems in Engineering can model dynamic systems whose structures are subject to random abrupt parameter changes resulting from component or interconnection failures, sudden environment changes, changing subsystem interconnections, and so forth [42][43][44][45]. A neural network has limited modes, which may jump from one to another at various periods.…”

Section: Introductionmentioning

confidence: 99%

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

Yogambigai

Ali

Zhu

et al. 2018

Mathematical Problems in Engineering

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The problem of exponential Lagrange stability analysis of Markovian jump neural networks with leakage delay and mixed timevarying delays is studied in this paper. By utilizing the Lyapunov functional method, employing free-weighting matrix approach and inequality techniques in matrix form, we establish several novel stability criteria such that, for all admissible parameter uncertainties, the suggested neural network is exponentially stable in Lagrange sense. The derived criteria are expressed in terms of linear matrix inequalities (LMIs). A numerical example is provided to manifest the validity of the proposed results.

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Exponential stability of Markovian jumping Cohen–Grossberg neural networks with mixed mode-dependent time-delays

Cited by 144 publications

References 37 publications

Stability analysis of quaternion‐valued Cohen‐Grossberg neural networks

Stability analysis of quaternion‐valued Cohen‐Grossberg neural networks

Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

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