Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, PR China.
Neural Netw. 2024 Feb;170:127-135. doi: 10.1016/j.neunet.2023.11.026. Epub 2023 Nov 10.
The exponential stabilization of stochastic neural networks in mean square sense with saturated impulsive input is investigated in this paper. Firstly, the saturated term is handled by polyhedral representation method. When the impulsive sequence is determined by average impulsive interval, impulsive density and mode-dependent impulsive density, the sufficient conditions for stability are proposed, respectively. Then, the ellipsoid and the polyhedron are used to estimate the attractive domain, respectively. By transforming the estimation of the attractive domain into a convex optimization problem, a relatively optimum domain of attraction is obtained. Finally, a three-dimensional continuous time Hopfield neural network example is provided to illustrate the effectiveness and rationality of our proposed theoretical results.
本文研究了具有饱和脉冲输入的随机神经网络在均方意义下的指数稳定性。首先，通过多面体表示法处理饱和项。当脉冲序列由平均脉冲间隔、脉冲密度和模式相关脉冲密度确定时，分别提出了稳定性的充分条件。然后，使用椭球和多面体分别估计吸引域。通过将吸引域的估计转化为凸优化问题，得到了一个相对最优的吸引域。最后，给出了一个三维连续时间 Hopfield 神经网络实例，以验证所提出的理论结果的有效性和合理性。
