Li Chuandong, Wu Sichao, Feng Gang Gary, Liao Xiaofeng
College of Computers, Chongqing University, Chongqing 400030, China.
IEEE Trans Neural Netw. 2011 Feb;22(2):323-9. doi: 10.1109/TNN.2010.2100084. Epub 2011 Jan 13.
This brief studies the global exponential stability of the equilibrium point of discrete-time delayed Hopfield neural networks (DHNNs) with impulse effects by using difference inequalities. We shall consider the stabilizing effects of impulses when the corresponding impulse-free DHNN is even not asymptotically stable. The obtained results characterize the aggregated effects of impulses and deviation of the impulse-free DHNN from its equilibrium point on the exponential stability of the whole system. It is shown that, because of effects of impulses, the impulsive discrete-time DHNN may be exponentially stable even if the evolution of impulse-free component deviates from its equilibrium point exponentially.
本文利用差分不等式研究了具有脉冲效应的离散时间延迟霍普菲尔德神经网络（DHNNs）平衡点的全局指数稳定性。当相应的无脉冲DHNN甚至不是渐近稳定时，我们将考虑脉冲的稳定作用。所得结果刻画了脉冲的聚集效应以及无脉冲DHNN与其平衡点的偏差对整个系统指数稳定性的影响。结果表明，由于脉冲的作用，即使无脉冲部分的演化以指数方式偏离其平衡点，脉冲离散时间DHNN仍可能是指数稳定的。
