Fixed-time synchronization of hybrid impulsive complex networks via improved stability analysis

This paper investigates the fixed-time (FXT) synchronization of complex networks (CNs) with hybrid impulses by providing new theoretical insights into FXT stability of impulsive systems. Firstly, some new FXT stability criteria are developed for impulsive systems via leveraging the distinctive features of concave functions. Unlike some existing works, where impulsive gains are usually assumed to be time-invariant, the considered impulses here can be time-varying and may be harmful to the stability of the system, thus making the obtained results more widely applicable. Secondly, as an application, by designing a novel controller, we investigate the FXT synchronization of CNs with hybrid impulsive gains. Different from traditional controllers, the controller utilizes hyperbolic sine functions instead of power functions, which requiring fewer parameters and feedback terms while effectively reducing the chattering effects. Finally, the theoretical results are verified through numerical examples.