Consensus of multi-agent system with communication delays by self-delay PD control

This paper deals with the consensus problem under communication network inducing delays. It has come to light that introducing a delay will lead in general to a reduction of the performance or instability. Therefore, investigating the control protocols for time-delay systems converging to consensus is important. In the present paper, we assume that each agent receives its own state information with a constant delay and receives the state information from its neighbors with different constant delays respectively. A new consensus protocol by introducing a self-PD control item is proposed. Then a sufficient condition based on the generalized Nyquist stability criterion and Gersgorin discs theorem for the convergence of the individual agents' states to a common value is derived. Also a specific expression of the consensus equilibrium which depends on the initial state of agents, the delays and PD feedback intensity is presented. Simulations are provided that demonstrate the effectiveness of the theoretical results.