This paper mainly explores the fixed-time and preassigned-time output synchronization of spatiotemporal networks with directed topology. Firstly, a kind of exponential-type control scheme associated with output feedback is developed. Subsequently, several sufficient criteria are established to ensure fixed-time output synchronization by utilizing the Lyapunov method and Taylor expansion. Moreover, the upper bound of convergence time is evaluated based on fixed-time stability theory. Furthermore, the preassigned-time output synchronization criteria are proposed by improving the fixed-time output controller, which incorporates a specified time parameter. Unlike previous forms, there are no stringent requirements imposed on the output matrix, whether semi-positive, non-singular or full rank in terms of columns. Finally, corresponding simulations are given to confirm the theoretical analysis.

中文翻译：

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具有定向拓扑的输出耦合时空网络的基于指数控制的固定/预分配时间同步


本文主要探讨有向拓扑时空网络的固定时间和预定时间输出同步。首先，开发了一种与输出反馈相关的指数型控制方案。随后，利用李雅普诺夫方法和泰勒展开，建立了几个充分的准则来确保固定时间输出同步。此外，基于固定时间稳定性理论评估了收敛时间的上界。此外，通过改进固定时间输出控制器，提出了预定时间输出同步准则，该控制器结合了指定的时间参数。与以前的形式不同，对输出矩阵没有严格的要求，无论是半正矩阵、非奇异矩阵还是满秩矩阵。最后给出了相应的仿真验证了理论分析。