Finite-time synchronization of complex dynamic networks with impulsive control and actuator saturation: An LMI approach

This paper investigates the finite-time synchronization (FTS) of complex dynamic networks (CDNs) with impulsive control subject to actuator saturation. We develop a novel method that integrates the impulsive comparison principle and improved convex hull representation lemma of saturated function to derive LMI-based sufficient conditions for FTS, which are easy to verify. We also estimate the admissible set of initial values to ensure the validity of the lemma. Unlike previous work, we relax the monotonicity assumption on the Lyapunov function, which broadens our results’ applicability. Moreover, we formulate and solve an optimization problem to enlarge the admissible set under the LMI constraints, using YALMIP toolbox in MATLAB software. Finally, several numerical examples are proposed to demonstrate our results’ effectiveness and superiority. •Unlike prior impulse CDN studies, we examine actuator limits and prove FTS with initial bounds.•We merge impulse theory with convex hull methods to achieve FTS under actuator saturation limits.•Our method allows non-monotonic Lyapunov functions, enabling broader initial value estimation.