Novel stability of cellular neural networks with interval time-varying delay

Hu, Liang; Gao, Huijun; Zheng, Wei Xing

doi:10.1016/j.neunet.2008.09.002

Cited by 104 publications

(53 citation statements)

References 26 publications

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“…Although the delay decomposition approach was extended to neural networks with time-varying delays [35], it should be noted out that the proposed method in [35] is based on the decomposition of the delay interval [−h 1 , 0], where h 1 is the lower bound of time-varying delay. It is clear that the delay decomposition idea can not applicable in [35] when h 1 = 0.…”

Section: Resultsmentioning

confidence: 99%

“…In order to obtain the more effective passivity conditions, we firstly develop the direct delay decomposition approach by dividing the delay interval [−h, 0] into multiple time-varying segments, which is more general than some existing delay decomposition approach [32][33][34][35]. Secondly, the novel Lyapunov-Krasovskii functional is constructed by choosing proper functionals with different weight matrices corresponding to different segments.…”

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confidence: 99%

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Improved Results on Passivity Analysis of Uncertain Neural Networks with Time-Varying Discrete and Distributed Delays

Chen

2009

Neural Process Lett

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In this paper, the passivity analysis problem is investigated for uncertain neural networks with time-varying discrete and distributed delays. Based on direct delay decomposition idea and free-weighting matrix approach, several new delay-dependent passive criterions are derived in terms of linear matrix inequalities (LMIs), which can be easily checked by the Matlab LMI toolbox. Numerical examples show that the obtained results improve some existing ones.

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Improved Results on Passivity Analysis of Uncertain Neural Networks with Time-Varying Discrete and Distributed Delays

Chen

2009

Neural Process Lett

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“…There is a more recent theorem (see [16] and also [25] for a slight variation of it) that can be considered as the generalization of the previous one, in the sense that the lower bound of the time delay is not equal to zero, as in most cases, but this delay is represented in two parts, a constant part 1 and a time varying part ( ) such that ( ) = 1 + ( ) under the condition 0 ( ) 2 − 1 . In this notation, we consider for simplicity that all the processing units have the same time delay function ( ), and that the time delay gets values in the interval 1 ( ) 2 .…”

Section: Proof the Proof Of The Above Theorem Is Based On Lemma 42mentioning

confidence: 99%

On the global stability of time delayed CNNs

Margaris

2011

Open Computer Science

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Abstract:The objective of this paper is the concise presentation of the most important and recent lemmas and theorems associated with the global asymptotic and exponential stability of the equilibrium point of time delayed cellular neural networks. For each theorem a short proof is given, so that the reader can understand its features and its relationships to other theorems. In the last section, the presented theorems are grouped according to their characteristics and the way they relate to one another, and some of them are demonstrated, in order to draw conclusions about their use.

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“…Methods for constructing a dedicated LKF include delaypartitioning idea [12][13][14][15][16][17][18][19][20], triple integral terms [16][17][18][19][20][21][22][23][24][25], more information on the activation functions [26], augmented vector [27,28], etc. The proposed methods for estimating the timederivative of LKF include: Park' inequality [29], Jensen's inequality [30], free-weighing matrices [31], and reciprocally convex optimization [32].…”

Section: Introductionmentioning

confidence: 99%

New delay-dependent stability criteria for recurrent neural networks with time-varying delays

et al. 2015

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a b s t r a c tThis work is concerned with the delay-dependentstability problem for recurrent neural networks with time-varying delays. A new improved delay-dependent stability criterion expressed in terms of linear matrix inequalities is derived by constructing a dedicated Lyapunov-Krasovskii functional via utilizing Wirtinger inequality and convex combination approach. Moreover, a further improved delay-dependent stability criterion is established by means of a new partitioning method for bounding conditions on the activation function and certain new activation function conditions presented. Finally, the application of these novel results to an illustrative example from the literature has been investigated and their effectiveness is shown via comparison with the existing recent ones.

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Novel stability of cellular neural networks with interval time-varying delay

Cited by 104 publications

References 26 publications

Improved Results on Passivity Analysis of Uncertain Neural Networks with Time-Varying Discrete and Distributed Delays

Improved Results on Passivity Analysis of Uncertain Neural Networks with Time-Varying Discrete and Distributed Delays

On the global stability of time delayed CNNs

New delay-dependent stability criteria for recurrent neural networks with time-varying delays

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