Delay effect on group consensus seeking of second-order multi-agent systems

Group consensus problem is investigated for the second-order multi-agent systems with communication delay under general directed topology, and stationary consensus protocols are proposed for two sub-groups. By using algebraic graph theory and matrix theory, consensus conditions are obtained for second-order multi-agent systems without time delay firstly. Based on frequency-domain analysis method, delay-dependent and delay-independent consensus conditions are gained for the agents with communication delay, respectively. Numerical simulations show the correctness of the results.