Consensus based second order discrete-time multi-agent systems formation control with time-delays

In this paper, a formation control problem is investigated for second-order discrete-time multi-agent systems with time delays and varying initial formation errors by means of consensus strategies. We derive a framework of it by using a distributed control scheme which is based on consensus with local formation errors. Through system decomposition and stability analysis, a sufficient condition is given to guarantee that the desired formation can be preserved with initial formation errors and time-delays by a set of dimension reduction LMIs. Simulation results illustrate the correctness and effectiveness of the theoretical results.