一类无界时滞细胞神经网络的全局指数稳定性

Exponential Stability of a Class of Cellular Neural Networks with Unbounded Delays

比例时滞是一种不同于无界分布时滞的无界时变时滞.比例时滞系统作为一种重要的数学模型在物理、生物系统与控制理论等领域有着重要的应用.本文通过变换yi(t)=xi(et),将一类具比例时滞细胞神经网络等价变换成一类具常时滞变系数的细胞神经网络.利用矩阵范数性质及不等式技巧,得到了保证该系统平衡点存在唯一与全局指数稳定的时滞独立与时滞依赖的充分条件.其中时滞依赖的充分条件依赖于比例时滞因子的大小.给出一个数值算例及仿真结果验证了所得结论的有效性和与以往文献相比较低的保守性.

The proportional delay is an unbounded time-varying delay, which is different from the unbounded distributed delays. The proportional delay system as an important mathematical model often plays important roles in some fields such as physics, biology systems and control theory. Through the transformation yi（t）=xi（et）, a class of cellular neural networks with proportional delays is transformed into a class of cellular neural networks with constant delays and variable coefficients, and they are equivalent. Using certain matrix norm properties and inequality technique, delay-independent and delay-dependent sufficient conditions are derived to ensure existence, uniqueness and global exponential stability of the system. In the system the delay-dependent sufficient condition depends on the size of proportional delay factor. A numerical example and its simulation result show that the obtained results are effective and less conservative than previously existing results.