基于自由权矩阵的时滞神经网络系统时滞相依全局稳定性分析

On the delay-dependent global stability analysis of delayed neural networks based on the free-weighting matrix method

在激励函数有界且满足扇区条件的情形下研究了一类同时具有时变时滞和无穷分布时滞的神经网络系统全局稳定性.通过构造一个包含更多信息的新的Lyapunov泛函,利用自由权矩阵更好地描述Newton-Leibniz公式中各项以及系统各项之间的关系,充分利用状态变量、时滞函数、状态变量以及Lyapunov泛函导数中出现的负项中隐藏的信息,并结合S-Procedure等方法以线性矩阵不等式(LMI)的形式给出了系统时滞相依全局指数稳定充分条件.文中结果去掉了以往文献对时变时滞函数的导数具有不超过1的上界的限制条件,具有更低的保守性,且利用Matlab工具箱极易验证条件的正确性,并推广改进了相关文献的结果.

The global stability of the neural networks with both time-varying and infinite distributed delays is studied based on the condition that the activation functions satisfy the sector condition. By constructing a new Lyapunov functional which contains more information, utilizing the free-weight matrices which can better describe the relations among the terms of Newton-Leibnitz formula and the system, taking advantage of the information hidden in the state variable, the time delay functions , the derivative of the state variable and the Lyapunov functional, combining with the S-procedure, a delay-dependent sufficient condition for guaranteeing the globally exponential stability of the system is derived in form of LMI, which can be easily checked by the Matlab toolbox. The result obtained in this article improves the previous ones on which it threw off the constraint that the derivative of the time-varying function has an upper bound no larger than 1 and is less conservative than the relevant ones.