一类非线性中立型方程的渐近稳定性

考虑由中立型方程所表述的神经网络系统的渐近稳定性问题,对现有的渐近稳定性判据做了改进.通过引入适当的Lyapunov-Krasovskii泛函,给出方程渐近稳定的时滞依赖性代数判据,该判据不仅依赖离散时滞,还依赖中立型时滞.另外,取消了很多文献中对箅子(L)中的参数α所作的限定(0＜|α|＜1),给出更为一般的结果,并且以线性矩阵不等式给出的充分条件,可以利用各种有效的凸优化算法进行计算.最后利用Matlab工具包给出的数值例子,说明了判据的有效性.

Abstract：

This work gives an improved criterion for asymptotical stability of a class of nonlinear neural networks described by nonlinear neutral differential equations. By introducing suitable Lyapunov-Krasovskii functional, a delay dependent criterion which not only depends on the discrete delays but also on the neutral delay is presented. This paper has also broken away from the assumption of 0＜ |α| ＜1,which is used in the operator (L) in many previous works. The sufficient condition is expressed in terms of linear matrix inequality. The criterion can be solved by various efficient convex optimization algorithms. In the end of the work, utilizing Matlab toolbox, the numerical example is presented to illustrate feasibility of the criterion and extensive of the results given in the work.

Asymptotic Stability on A Class of Nonlinear Neutral Equations