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This paper investigates the synchronization of complex dynamic networks with time-varying delay and general semi-Markovian jump. The general transition rates include completely unknown and uncertain but bounded as two special cases. First, by introducing auxiliary vectors with a few nonorthogonal polynomials, two free-matrix-based integral inequalities are developed, which encompass some existing ones as special cases. Second, an integral- based delay-product-type Lyapunov-Krasovskii functional is constructed, which fully considers the information of time delay. By utilizing a deley-dependent controller, two sufficient conditions are derived to realize the global stochastic mean-square synchronization by employing the established inequalities to evaluate the infinitesimal generator of the functional. This paper takes all possibilities into consideration and divides the general transition rates into five cases, which is never investigated before. Finally a numerical example is given to show the effectiveness and practicality of the presented method. [ABSTRACT FROM AUTHOR]

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]

This paper investigates the stochastic stability of fuzzy Markovian jumping neural networks with mixed delays in mean square. The mixed delays include time-varying delay and continuously distributed delay. By using the Lyapunov functional method, Jensen integral inequality, the generalized Jensen integral inequality, linear convex combination technique and the free-weight matrix method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which do not require the differentiability 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]