Fixed-Time Synchronization of Leaderless and Leader-Following Multi-Agent Networks With Delayed Impulses

This work investigates the fixed-time synchronization (FXTS) problem of leaderless (LL) and leader-following (LF) multi-agent neural networks (MANs) with time-varying delays using an impulsive control approach. Using Lyapunov-Razumikhin theory, FXTS for LL and LF MANs is studied by considering synchronizing and desynchronizing delayed impulses. By constructing the novel control scheme that includes the impulse information, some sufficient conditions for FXTS of MANs are derived by using linear matrix inequalities. Additionally, impulse-dependent settling time (ST) is estimated in synchronizing and desynchronizing impulses, implying that both LL and LF MANs converge to the equilibrium point within the finite-time. The proposed results demonstrate that synchronizing impulses reduces the upper bound of the ST while destabilizing impulses can extend it. Theoretical findings are further validated through the numerical simulations that illustrating the impact of stabilizing and destabilizing impulses on the upper bound of the ST.