State Feedback Consensus for Multi-Agent System with Multiple Time-Delays

In this paper, we study the multi-agent system to achieve a faster consensus with multiple time-delays under a directed asymmetric information exchange topology. We first assume that an agent processes its own state information with self-delay and receives state information from its neighbors with communication delays. Based on state proportion derivative feedback, the improved consensus protocol can accelerate the system to achieve a consensus. A sufficient condition for reaching consensus is then derived based on the Nyquist stability criterion and frequency domain analysis. In addition, a specific form of consensus equilibrium is obtained which is influenced by the initial states of agents, time-delays and state feedback intensity. Finally, simulations are presented to verify the validity of the theoretical results.