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This paper investigates the problem of stability of fuzzy neural networks with time-varying and continuously distributed delays under impulsive perturbations. Two new delay-dependent criteria are obtained in terms of linear convex combination technique, the reciprocal convex lemma, Wirtinger-based integral inequality, and the quadratic convex combination method. The first presented criterion does not require all the symmetric matrices involved in the employed quadratic Lyapunov–Krasovskii functional to be positive definite. Furthermore, the conservatism of delay-dependent stability conditions can be reduced due to the relaxation on the positive-definiteness of some Lyapunov matrices. It is shown numerically that the stability criteria proposed in this paper are less conservative than some of the latest results in the literature. [ABSTRACT FROM AUTHOR]

The stability is investigated for a kind of fuzzy cellular neural networks with time-varying and continuously distributed delays under impulsive perturbations. When the Wirtinger-based integral inequality is applied to partitioned integral terms in the derivation of matrix inequality conditions, a new kind of linear combination of positive functions emerges weighted by the inverses of cubic convex parameters. This paper proposes an efficient method called third-order reciprocally convex approach to manipulate such a combination by extending the reciprocal convex technique. By utilizing Briat lemma and reciprocal convex approach, this paper derives several novel sufficient conditions to ensure the global asymptotic stability of the equilibrium point of the considered networks. Based on the derived criteria, a lower-bound estimation can be obtained of the largest stability interval for a class of fuzzy cellular neural networks under impulsive perturbations. Simulation examples demonstrate that the presented method can significantly reduce the conservatism of the existing results, and lead to wider applications. [ABSTRACT FROM AUTHOR]

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]

This paper investigates the global asymptotic stability of a kind of fuzzy cellular neural networks with mixed delays under impulsive perturbations. The mixed delays include constant delay in the leakage term (i.e., 'leakage delay'), time-varying delays, and continuously distributed delays. By using the quadratic convex combination method, reciprocal convex approach, Jensen integral inequality, and linear convex combination technique, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered 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 and less conservativeness of our theoretical results over existing literature. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates a class of mixed recurrent neural networks with time delay in the leakage term under impulsive perturbations. The mixed time-delays consist of both discrete and distributed delays. By using the Lyapunov functional method, linear matrix inequality approach and general convex combination technique, two novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the networks. The proposed results, which do not require the boundedness, differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Moreover, they indicate that the stability behavior of neural networks is very sensitive to the time delay in the leakage term. Finally, numerical examples are given to demonstrate the effectiveness of our theoretical results. [Copyright &y& Elsevier]