This paper investigates the problem for exponential stability of stochastic Hopfield neural networks involving multiple discrete time-varying delays and multiple distributed time-varying delays. The exponential stability of such neural systems has not been given much attention in the past literature because this type of neural systems cannot be transformed into the vector forms and it is difficult to derive the easily verified stability conditions expressed in terms of the linear matrix inequality. Therefore, this paper tries to establish the easily verified sufficient conditions of the linear matrix inequality forms to ensure the mean-square exponential stability and the almost sure exponential stability for this type of neural systems by constructing a suitable Lyapunov-Krasovskii functional and inequality techniques. Four examples are provided to demonstrate the effectiveness of the proposed theoretical results and compare the established stability conditions to the previous results.
Citation: Qinghua Zhou, Li Wan, Hongbo Fu, Qunjiao Zhang. Exponential stability of stochastic Hopfield neural network with mixed multiple delays[J]. AIMS Mathematics, 2021, 6(4): 4142-4155. doi: 10.3934/math.2021245
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This paper investigates the problem for exponential stability of stochastic Hopfield neural networks involving multiple discrete time-varying delays and multiple distributed time-varying delays. The exponential stability of such neural systems has not been given much attention in the past literature because this type of neural systems cannot be transformed into the vector forms and it is difficult to derive the easily verified stability conditions expressed in terms of the linear matrix inequality. Therefore, this paper tries to establish the easily verified sufficient conditions of the linear matrix inequality forms to ensure the mean-square exponential stability and the almost sure exponential stability for this type of neural systems by constructing a suitable Lyapunov-Krasovskii functional and inequality techniques. Four examples are provided to demonstrate the effectiveness of the proposed theoretical results and compare the established stability conditions to the previous results.
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Qinghua Zhou, Li Wan, Hongbo Fu, Qunjiao Zhang. Exponential stability of stochastic Hopfield neural network with mixed multiple delays[J]. AIMS Mathematics, 2021, 6(4): 4142-4155. doi: 10.3934/math.2021245
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