基于忆阻时滞神经网络的耗散研究

针对一类基于忆阻时滞神经网络的耗散问题，提出一种结合倒凸技术和Wirtinger积分不等式的耗散方法。首先，应用微分包含和集值映射理论，将忆阻时滞神经网络转化成传统的时滞神经网络；接着，构造含有时滞系数的状态向量2次项和3重积分项的Lyapunov-Krasovskii泛函（LKF），应用倒凸技术和Wirtinger积分不等式估计LKF微分，得到了确保时滞神经网络严格耗散的时滞依赖条件，这些条件可以用线性矩阵不等式形式表示并且易于用Matlab软件实现。将该方法推广到研究时滞神经网络无缘分析问题中。在数值例子中，针对不同的时滞变化率上界，与现有文献的最优耗散性能指标进行比较，实验结果表明，本文方法将其提高了5%。另外，在相同时滞条件下，仿真分别给出了神经网络系统有外部输入和无外部输入的状态轨迹，由仿真结果可以看出外部输入的存在的确破坏系统稳定性。

Dissipativity Research on Memristor-based Neural Networks with Time-varying Delays

In order to solve the problem of dissipativity for memrisor-based neural networks with time-varying delay,a new method was proposed,which combined a reciprocally convex technique with a Wirtinger-based integral inequality.First,to convert memristive neural networks into the conventional neural networks,differential inclusions and set-valued maps were applied.Then,based on the construction of a Lyapunov-Krasovskii functional with a time-delay coefficient quadratic term of the state vector and a triple integral term,the delay-dependent conditions in terms of linear matrix inequalities were obtained to assure the neural networks strictly dissipative.The derivative of Lyapunov-Krasovskii functional is estimated by using a reciprocally convex technique and a Wirtinger-based integral inequality,which can be easily solved via Matlab.Moreover,the proposed method was extended to investigate the passivity analysis of the considered systems.Finally,the comparisons with the available references showed that this method gives an improvement of 5% in optimal dissipativity performances for various upper bounds of delay variation in numerical examples.In addition,in the same time-delay case,the simulations provided the state trajectories of the neural network system with external input and without external input,respectively.It was shown that the existence of external input was certain to destroy the stability of the system from the simulation results.