Nonrestricted impulsive sampling control for synchronization of uncertain neural networks with hybrid discrete-delayed and distributed-delayed couplings: A new Halanay-like impulsive differential comparative lemma

This article discusses the exponential synchronization challenge for uncertain neural networks with non-delayed coupling, discrete-delayed and distributed-delayed couplings. To tackle the effect of various couplings and large delays on network stabilization, a new Halanay-like impulsive differential comparative lemma is established by strict mathematical induction and reductio ad absurdum, which relaxes the conventional limitations on coefficient constraints. Based on the novel comparative lemma and Lyapunov function method, exponential synchronization criteria with the Kronecker product for the studied neural networks can be derived using a novel impulsive control protocol with current information and historical state communication. Traditional impulsive sampling control mechanisms require each sampling delay to be less than the sampling interval. Unlike conventional works, the impulsive control protocol and comparative lemma proposed in this study ensure the successful implementation of exponential synchronization in the considered neural networks, regardless of whether the impulsive sampling delay is larger or smaller than the sampling interval. In other words, our impulsive control intervals are nonrestricted by the size of sampling delays, which means the impulsive sampling scheme in this paper can effectively save control costs and increase communication security in practical applications.