Abstract This paper focuses on state estimation problem for discrete-time high-order neural networks with time-varying delays. First, the delay-dependent global exponential stability criterion of the error system is derived. Then, the state observer is designed by using the generalized inverse theory of matrices. Last, two numerical examples are given to illustrate the validity of the theoretical results. The method proposed in this paper has two advantages: (i) it is directly based on the definitions of global exponential stability and Moore–Penrose inverse of matrix, which avoids the construction of Lyapunov–Krasovskii functional; (ii) the obtained stability criteria contain only several simple matrix inequalities, which are easier to solve. More valuable, this paper fills in the gaps in designing state observers for discrete-time high-order neural network models.

中文翻译：

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具有时变延迟的离散时间高阶神经网络的状态估计

摘要 本文重点研究具有时变延迟的离散时间高阶神经网络的状态估计问题。首先，推导出误差系统的时延相关全局指数稳定性判据。然后，利用广义矩阵逆理论设计状态观测器。最后，给出了两个数值例子来说明理论结果的有效性。本文提出的方法有两个优点：(i)直接基于全局指数稳定性和矩阵的Moore-Penrose逆的定义，避免了Lyapunov-Krasovskii泛函的构建；(ii) 获得的稳定性准则只包含几个简单的矩阵不等式，更容易解决。更有价值，