On global exponential stability of generalized stochastic neural networks with mixed time-delays

Abstract This paper is concerned with the global exponential stability analysis problem for a general class of stochastic neural networks with mixed time-delays. The mixed time-delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed stochastic neural network is exponentially stable in the mean square in the presence of both the discrete and distributed delays. By employing a new Lyapunov–Krasovskii functional and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria of the exponential stability. Furthermore, the main results are specialized to deal with the analysis problem for the global asymptotic stability within the same LMI framework. The proposed criteria can be readily checked by using some standard numerical packages such as the Matlab LMI toolbox. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria.

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