具有变时滞Cohen-Grossberg神经网络全局稳定性分析

Analysis on global stability of Cohen-Grossberg neural networks with time-varying delay

通过选取一个新颖的Lyapunov-Krasovskii泛函和引入与系统等价的描述系统,利用一些自由权矩阵和不等式适当的放大,在Lyapunov-Krasovskii泛函方法的基础上,讨论了具有变时滞Cohen-Grossberg神经网络的全局稳定性问题并得到了2个时滞相关的渐近稳定性准则.所得到的稳定性准则以线性矩阵不等式(LMI)的形式给出,能够用Matlab工具箱LMI很容易地进行检验.且变时滞导函数只要有上界而不必小于1和系统激励函数的限制条件较现有文献中的条件要弱,这拓展了现有的结论.在最后的数值例子中,计算结果说明所得结论较以往的方法有很大改善.

Through choosing a novel Lyapunov-Krasovskii functional, introducing the equivalent descriptor form of addressed systems, employing some free-weighting matrices and appropriate enlargement of inequalities, the global stability of Cohen-Grossberg neural networks with time-varying delays is investigated and two delay-dependent stability criteria are obtained based on the Lyapunov-Krasovskii functional method. The criteria are presented in terms of LMIs, which can be easily checked by the LMI （linear matrix inequality） in the Matlab Toolbox. Additionally, the derivative of the time-varying delay only request an upper limitation but not necessarily less than 1 and the activation functions are of more general descriptions, which generalize those existing results. In the numerical example, the comparing results can illustrate that the obtained method is an improvement over the earlier ones.