神经网络指数稳定性分析的一种方法

An approach to exponential stability of neural networks

提出了一种非线性测度 ,利用这种非线性测度研究了一类神经网络的局部指数稳定性和全局指数稳定性 .得到了保证神经网络的平衡点唯一、全局和局部指数稳定的一些充分条件 ,导出了神经网络有多于一个平衡点的必要条件 .同时得到神经网络任意两个解的差的估计式 ,以及神经网络指数收敛的收敛率和神经网络局部指数稳定的吸引区域的估计 .所得结果是新的且不同于已有文献 。

A concept nonlinear measure was introduced to analyze global and local exponential stability of neural networks. Sufficient criteria were obtained to guarantee that the equilibrium point of neural networks was unique, globally and locally exponentially stable. A necessary condition was presented to guarantee that there existed more than one equilibrium point. The estimate on deviation of two solutions of the neural network was derived, and the estimate on the exponential convergent rate and the estimate on the attractive region of exponential convergence were obtained. The presented results are new, different from the existed ones and practical.