State-dependent Impulsive Control for Consensus of Multi-agent Systems

This paper aims to investigate the consensus of multi-agent systems, where each agent runs hopfied-type neural networks, by means of the state-dependent impulsive control. The challenge comes from the fact that the occurrence of impulse varies according to the state of the agent, which means it is hard to predict when an impulse occurs. To solve this problem, we try to transform the impulsive system from state-dependent to fixed-time. In order to do that, we first construct a global consensus error state-dependent with a multi-agent system according to the impulsive consensus protocol. Then we use the B-equivalence method to form a comparison impulsive system of fixed-time impulsive sequence. Using Lyapunov stability theory, we prove that these two systems have the same stability. So we establish sufficient consensus conditions of multi-agent system by analyzing the comparison system. We perform extensive evaluations to validate the correctness of theoretical results and the effectiveness of the state-dependent impulsive consensus protocol.