Finite-time synchronization of complex dynamical networks with parametric uncertainties under delayed impulsive control

Abstract This study investigates the problem of finite-time synchronization (FTS) in complex dynamical networks (CDNs) with time-varying delays and parametric uncertainties under delayed impulses. A control strategy incorporating delayed impulses is developed, considering the combined effects of time-delays and impulses. Constructing suitable Lyapunov–Krasovskii functionals establishes sufficient conditions for FTS in terms of linear matrix inequalities. The proposed method ensures that CDNs achieve FTS even in the presence of parametric uncertainties, as the derived criteria guarantee that the error systems achieve FTS, that is the error state bounded within a prescribed finite-time. Finally, numerical examples and corresponding simulations are provided to demonstrate the effectiveness and robustness of the proposed approach.