Potential impacts of delay on pinning impulsive secure synchronization control of delayed networks

This paper explores the impact of delays on the secure and anti-disturbance synchronization of time-delayed networks under a pinning impulsive control strategy. An exponential-type Lyapunov function and a novel impulsive delay inequality are proposed, extracting and incorporating the information of time delay existing in continuous dynamics into Lyapunov-based conditions. A probabilistic channel failure model is used to analyze the impact of deception attacks and disturbances. Sufficient conditions for mean square bounded synchronization (MSBS) are derived, showing that appropriate delays might mitigate attacks and accelerate convergence. The minimum pinning control threshold to achieve MSBS is derived from the attacks. The factors affecting error bounds are discussed. Numerical simulations on small-world networks, multi-agent systems, and Chua's circuit validate the theory.