Abstract
This paper derives some sufficient conditions for exponential stability in the mean square of stochastic discrete-time delayed Hopfield neural networks (DHNN) with impulse effects. The Lyapunov–Krasovskii stability theory, Halanay inequality, and linear matrix inequality (LMI) are employed to investigate the problem. It is shown that the impulses in certain regions might preserve the stability property of the DHNN when the impulses-free part converges to its equilibrium point. Moreover, the feasible interval of the jump operator is also derived.
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The work described in this paper was partially supported by the Fundamental Research Funds for the Central Universities of China (Project No. CDJXS11180015, CDJZR10185501, CDJXS10182215), the National Natural Science Foundation of China (Grant No.60974020, 60972155).
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Duan, S., Hu, W., Li, C. et al. Exponential Stability of Discrete-Time Delayed Hopfield Neural Networks with Stochastic Perturbations and Impulses. Results. Math. 62, 73–87 (2012). https://doi.org/10.1007/s00025-011-0131-z
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DOI: https://doi.org/10.1007/s00025-011-0131-z