一种新的时滞细胞神经网络全局渐近稳定性准则

研究了一类具有时滞的细胞神经网络全局稳定性问题。首先,提出所研究的时滞细胞神经网络模型、系统激活函数所需满足的条件及本文需要用到的引理。然后,将所研究的系统通过一个等式进行线性变换,在定义一个与系统相关的积分操作基础上讨论时滞细胞神经网络的全局渐近稳定性。与早期的文献结果相比,本文所得结果具有更少保守性,并且该条件是与时滞相关的。本文所得到的稳定性准则可以很容易地求出系统稳定的时滞上界,进而可以很容易得到时滞无关稳定性结果。最后,用一个数值例子证明本文所得的稳定性条件是有效的。

New Global Asymptotic Stability Condition of Cellular Neural Networks with Delays

In this paper the global asymptotic stability of cellular neural networks with delays is investigated by utilizing Lyapunov functional method and the linear matrix inequality(LMI) technique.Distinct difference from other analytical approaches lies in "linearization" of the neural network model,by which the considered neural network model is transformed into a linear system.Then,so called parameterized first-order model transformation is used to transform the linear system.We establish novel sufficient conditions for the cellular neural networks to be globally asymptotic stable by utilizing Lyapunov-Krasovskii functional method and some well-know inequalities.Compared with the earlier results in the literature,these results are less restrictive and conservative.The advantage of the proposed approaches is that resulting stability criteria can be used efficiently via existing numerical convex optimization algorithms, such as the interior-point algorithms for solving LMIs.The results are dependent on the time delay.Numerical example is given to show the effectiveness of our proposed method.