Stochastic synchronization for an array of hybrid neural networks with random coupling strengths and unbounded distributed delays

Abstract This paper investigates the globally asymptotic synchronization for hybrid neural networks with random coupling strengths and mixed time-delays in the mean square. By employing a novel augmented Lyapunov–Krasovskii functional (LKF), applying the theory of Kronecker product of matrices, Barbalat’s Lemma and the auxiliary function-based integral inequalities, several novel delay-dependent conditions are established to achieve the globally stochastic synchronization for the hybrid coupled neural networks. Two presented criteria do not require all the symmetric matrices involved in the employed quadratic LKF 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. Finally, two numerical examples with simulation are provided to illustrate the effectiveness of the presented criteria.

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