Exponential control-based fixed/preassigned-time synchronization of output-coupled spatiotemporal networks with directed topology

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.