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This paper investigates the synchronization problem for a class of chaotic neural networks with discrete and unbounded distributed time delays under stochastic perturbations. Firstly, based on the Wirtinger-based double integral inequality, two novel inequalities are proposed, which are multiple integral forms of the Wirtinger-based integral inequality. Next, by applying the Jensen-type integral inequality for stochastic case and combining the Jensen integral inequality with the reciprocally convex combination approach, a delay-dependent criterion is developed to achieve the synchronization for the stochastic chaotic neural networks in the sense of mean square. In the case of no stochastic perturbations, by applying the reciprocally convex combination approach for high order case and a free-matrix-based inequality, novel delay-dependent conditions are established to achieve the synchronization for the chaotic neural networks. All the results are based on dividing the bounding of activation function into two subintervals with equal length. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

For the first time, this paper investigates the global asymptotic stability of stochastic fuzzy neural networks with mixed delays and Markovian jumping under impulsive perturbations in mean square. The mixed delays include time-varying delay and continuously distributed delay. By using stochastic analysis method, linear convex combination technique, Jensen integral inequality and the free-weight matrix method, a novel sufficient condition is derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed result, which is expressed in terms of linear matrix inequalities, can be easily checked via Matlab software. Finally, a numerical example is given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature. [ABSTRACT FROM AUTHOR]

This paper investigates the stochastic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square. By using the reciprocal convex combination approach, Jensen and Jensen-type integral inequality, linear convex combination technique and the free-weight matrix method, several novel mode and delay-dependent sufficient conditions are derived to ensure the stochastic stability of the equilibrium point of the considered networks in mean square. The proposed results can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature. [ABSTRACT FROM AUTHOR]

This paper investigates the stability of switched Hopfield neural networks of neutral type with time-varying delay and continuously distributed delay. By using the quadratic convex combination method, the reciprocal convex combination approach, some generalized Jensen integral inequalities, and the free-weight matrix method, several novel sufficient conditions are derived to ensure the asymptotic stability of the equilibrium point of the considered networks. The proposed results, which do not require the differentiability of the activation functions, can be easily checked via Matlab software. Finally, three numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature. [ABSTRACT FROM AUTHOR]

This paper studies the globally asymptotic stability of neutral-type impulsive neural networks with discrete and bounded continuously distributed delays. By using the Lyapunov functional method, quadratic convex combination approach, a novel Gu's Lemma, Jensen integral inequality and linear convex combination technique, several novel sufficient conditions are derived to ensure the globally asymptotic stability of the equilibrium point of the networks. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

SUMMARY The exponential stability problem is investigated for a class of uncertain stochastic neural networks with discrete and unbounded distributed time delays. Two types of uncertainty are considered: one is time-varying structured uncertainty, whereas the other is interval uncertainty. With the application of the Jensen integral inequality and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent criteria are developed to achieve the exponential stability in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve fewer free weighting matrices, the computational burden is largely reduced. Three numerical examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the exponential stability problem for a class of stochastic Cohen-Grossberg neural networks with discrete and unbounded distributed time delays. By applying the Jensen integral inequality and the generalized Jensen integral inequality, several improved delay-dependent criteria are developed to achieve the exponential stability in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve fewer free weighting matrices, the computational burden is largely reduced. Three numerical examples are provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the existence, uniqueness and globally robust exponential stability for a class of uncertain neutral-type Cohen–Grossberg neural networks with time-varying and unbounded distributed delays. Based on Lyapunov–Krasovskii functional, by involving a free-weighting matrix, using the homeomorphism mapping principle, Cauchy–Schwarz inequality, Jensen integral inequality, linear matrix inequality techniques and matrix decomposition method, several delay-dependent and delay-independent sufficient conditions are obtained for the robust exponential stability of considered neural networks. Two numerical examples are given to show the effectiveness of our results. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, the state estimation problem is investigated for neural networks with time-varying delays as well as general activation functions. By applying the Finsler''s Lemma and constructing appropriate Lyapunov–Krasovskii functional based on delay partitioning, several improved delay-dependent conditions are developed to estimate the neuron state with some available output measurements such that the error-state system is global asymptotically stable. It is established theoretically that one special case of the obtained criteria is equivalent to some existing result with same conservatism but including fewer LMI variables. As the present conditions involve no free-weighting matrices, the computational burden is largely reduced. Two examples are provided to demonstrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: The problem of global asymptotic stability analysis is studied for a class of cellular neural networks with time-varying delay. By defining a Lyapunov–Krasovskii functional, a new delay-dependent stability condition is derived in terms of linear matrix inequalities. The obtained criterion is less conservative than some previous literature because free-weighting matrix method and the Jensen integral inequality are considered. Three illustrative examples are given to demonstrate the effectiveness of the proposed results. [Copyright &y& Elsevier]