Synchronization for coupling delayed complex dynamical networks in time-square-dependent looped-functionals via a new sampled-data control approach

This paper proposes a novel sampled-data control (SDC) approach for addressing synchronization problems in complex dynamical networks (CDNs) with coupling delays in time-square-dependent looped-functionals (TSDLFs). The proposed method introduces a sampling-time-dependent control signal to achieve synchronization while considering coupled time-varying delays and uncertainties in CDNs. To ensure asymptotic stability, new Lyapunov functionals are constructed, including TSDLFs and two-sided looped functionals, effectively utilizing information over the intervals $[t_k,t]$ and $[t,t_{k+1})$. Sufficient conditions are derived to guarantee the asymptotic stability of the error states. A numerical example based on Chua’s circuits demonstrates the effectiveness and superiority of the proposed method.