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This study focuses on the exponential synchronization problem of complex networks (CNs) with time delays and impulse disturbances. Unlike existing research, an adaptive state feedback controller with time-varying adaptive gain is designed and only implemented on partial nodes. By constructing a Lyapunov-Krasovskiy (L-K) functional combined with linear matrix inequalities (LMIs), a sufficient condition is derived, which guarantees exponential synchronization of complex networks under pinning control. Notably, designing an L-K functional to handle adaptive gain remains a technical challenge. The validity of main result is verified by numerical simulations of Chua’s circuits. During simulations, by adjusting parameters in the LMI conditions, we ensure the derived sufficient condition is satisfied and observe whether all node trajectories converge rapidly to the synchronization manifold. Furthermore, comparative analysis of synchronization performance under different initial adaptive gain values and impulse disturbance intensities demonstrates the controller’s robustness to parameter variations, providing theoretical foundations and technical references for synchronization control of real-world complex network systems.
Adaptive control; pinning control; impulsive disturbances; Lyapunov-Krasovskii functional; synchronization
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Synchronization of Complex Networks with Time Delays and Impulsive Disturbances via Pinning Adaptive Control
How to cite this paper: Mingyu Li. (2026) Synchronization of Complex Networks with Time Delays and Impulsive Disturbances via Pinning Adaptive Control. Journal of Applied Mathematics and Computation, 10(1), 47-58.
DOI: http://dx.doi.org/10.26855/jamc.2026.03.006