In this article, we considered the fixed-time stability (FXT) of a type of discontinuous dynamical system. First, we introduced some new FXT stability results via variable substitutions and using inequality techniques, which are more accurately estimate the upper bound of settling time (ST). Then, based on the established results and using the differential inclusion theory, we investigated the FXT synchronization of a type of general neural networks (NNs) with state-dependent switching coefficients and discontinuous neuron activation functions via introducing a type of discontinuous controller which is more simple compared to existing results. In addition, the estimated upper bound of ST shown to be independent to the initial values of considered drive-response networks, and it is much smaller and nearer to the real synchronization time than those given in the previously published works. Lastly, two numerical examples are given to demonstrate the feasibility of our derived theoretical results. We believe that the results of this article can give some new insights for the FXT stabilization and FXT synchronization analysis of state-dependent switching dynamics with or without discontinuous right-hand sides.

中文翻译：

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改进的固定时间稳定性结果及其在具有状态相关切换的不连续神经网络同步中的应用

在本文中，我们考虑了一类不连续动力系统的固定时间稳定性 (FXT)。首先，我们通过变量替换和使用不等式技术引入了一些新的 FXT 稳定性结果，它们可以更准确地估计稳定时间 (ST) 的上限。然后，基于已建立的结果，并使用微分包含理论，我们通过引入一种更简单的不连续控制器，研究了具有状态相关切换系数和不连续神经元激活函数的一类通用神经网络 (NN) 的 FXT 同步。与现有结果相比简单。此外，ST 的估计上限显示出与所考虑的驱动响应网络的初始值无关，并且它比以前发表的作品中给出的更小更接近真实的同步时间。最后，给出了两个数值例子来证明我们推导出的理论结果的可行性。我们相信，本文的结果可以为具有或不具有不连续右侧的状态相关切换动力学的 FXT 稳定和 FXT 同步分析提供一些新的见解。