基于二次型的CNN全局渐近稳定性研究

Research of Global Asymptotic Stability for CNN Based on Quadratic Form

细胞神经网络稳定性目前已经在图像处理、视频通信和最优控制等领域得到了一定的应用,因此进行稳定性的研究具有重要的意义,如何选择合理的参数模板是研究稳定性的关键问题。运用Lyapunov第二方法对细胞神经网络的全局渐近稳定性进行分析,通过构造出一个较好的Lyapunov函数来得到判定系统全局渐近稳定的一组新的充分条件。该条件改进了已有的结论,进一步推导和完善了系统全局渐近稳定平衡点为原点时的充分条件,经过数值仿真实验验证了其有效性和可行性。

Stability of cellular neural networks is significant because it has been used in a certain application areas as ima-ge processing,video communication,optimal control and so on.How to choose a reasonable template of the parameters is the key issue of stability researches.Lyapunov second method was used to analyze the global asymptotic stability of cellular neural networks,and a better Lyapunov function was constructed to receive a new sufficient condition for determining the global asymptotic stability of the system.The condition improves previous results and further derives a sufficient condition when original point is equilibrium point.Numerical simulations show their effectiveness and feasibility.