Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

Rakkiyappan, R.; Balasubramaniam, P.

doi:10.1016/j.nahs.2009.02.008

Cited by 50 publications

(12 citation statements)

References 28 publications

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“…Construct the candidate Lyapunov function as V.x, i/ D x T P i x, where P i is a symmetric positive definite matrix and i 2 S. It is obvious that condition (i) of Theorem 3.1 holds. On one hand, we note that by the Schur complement, matrix inequalities (26) and (27) are equivalent to the following matrix inequalities respectively:…”

Section: Proofmentioning

confidence: 99%

Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach

Cheng

He³

2017

Math Methods in App Sciences

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In this paper, we aim to investigate the exponential stability of general hybrid stochastic functional differential systems with delayed impulses. By using the average impulsive interval and the Lyapunov function method, we derive some sufficient conditions for exponential stability, which are less conservative than those existing results based on the supremum or infimum of impulsive interval and more convenient to be applied than those Razumikhin‐type conditions in the literature. Meanwhile, we show that unstable hybrid stochastic delay differential systems, both linear and nonlinear, can be stabilized by suitably impulsive sequence. Finally, two examples are discussed to illustrate the effectiveness and advantages of the obtained results. Copyright © 2017 John Wiley & Sons, Ltd.

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Section: Proofmentioning

confidence: 99%

Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach

Cheng

He³

2017

Math Methods in App Sciences

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“…Remark 2: In the literature of Yuan et al (2006), Rakkiyappan andSu and, the term À Â R t tÀ%ðtÞ f ðxðsÞÞds Ã T Â T Â R t tÀ%ðtÞ f ðxðsÞÞds Ã was always employed to estimate À R t tÀ% m % m f T ðxðsÞÞTf ðxðsÞÞds and the terms such as À R t tÀ% m ½% m À %ðtÞ f T ðxðsÞÞTfðxðsÞÞds and À R tÀ%ðtÞ tÀ% m % m Â f T ðxðsÞÞTfðxðsÞÞds have not been taken into consideration. In (12), those previously ignored terms have been added to estimate _ V 4 ðxðtÞÞ.…”

Section: Yðsþdsmentioning

confidence: 99%

“…Recently, the stability of neural networks with distributed delay has been investigated widely and, furthermore, researchers have proposed some important results on CGNNs with distributed delay (Song and Cao 2006;Yuan et al 2006;Lou and Cui 2007;Fei 2008, Meng et al 2008;Rakkiyappan and Balasubramaniam 2009;Su and Chen 2009;Wang, Guo, and Xu 2009), in which one kind of distributed delay is bounded while the other is unbounded. However, as for distributed delay…”

Section: Introductionmentioning

confidence: 99%

Further stability analysis on Cohen–Grossberg neural networks with time-varying and distributed delays

Song

Fei

2011

International Journal of Systems Science

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The article is concerned with asymptotical stability for Cohen-Grossberg neural networks with both interval time-varying (0 0 (t) m ) and distributed delays, in which two types of distributed delays are treated: one is bounded while the other is unbounded. Through partitioning the delay intervals [0, 0 ] and [ 0 , m ], and choosing two augmented Lyapunov-Krasovskii functionals, some sufficient conditions are obtained to guarantee the global stability by employing the simplified free-weighting matrix method and convex combination. These stability criteria are presented in terms of linear matrix inequalities (LMIs) and can be easily checked by resorting to LMI in Matlab toolbox. Finally, three numerical examples are given to illustrate the effectiveness and reduced conservatism of the theoretical results.

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“…It is known that a Markovian jump stochastic neural network is more complicated and comprises a general stochastic neural network as its special case. Owing to the practical importance, many journal papers have recently devoted to study the stability analysis issue for Markovian jump neural networks [1,13,18,27,28,31,33,35,36,[38][39][40]. However, up to now, the synchronization problem for Markovian jump neural networks has received little research attention, despite its practical importance.…”

Section: Introductionmentioning

confidence: 99%

pth moment exponential synchronization for stochastic delayed Cohen–Grossberg neural networks with Markovian switching

2011

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This paper is a contribution to the analysis of the pth moment exponential synchronization problem for a class of stochastic delayed Cohen-Grossberg neural networks with Markovian switching. The jumping parameters are determined by a continuous-time, discrete-state Markov chain, and the delays are timevarying delays.By using the Lyapunov-Krasovskii functional, stochastic analysis theory, a generalized Halanay-type inequality as well as output coupling with delay feedback control technique, some novel sufficient conditions are derived to achieve complete pth moment exponential synchronization of the addressed neural networks. In particular, the traditional assumptions on the differentiability of the time varying delay and the boundedness of its derivative are removed in this paper. The results obtained in this paper generalize and improve many known results. Moreover, a numerical example and its simulation are also provided to demonstrate the effectiveness and applicability of the theoretical results.

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Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

Cited by 50 publications

References 28 publications

Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach

Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach

Further stability analysis on Cohen–Grossberg neural networks with time-varying and distributed delays

pth moment exponential synchronization for stochastic delayed Cohen–Grossberg neural networks with Markovian switching

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