The group-delay consensus for second-order multi-agent systems by piecewise adaptive pinning control in part of time interval

This paper addresses the group-delay consensus of second-order nonlinear multi-agent systems by piecewise adaptive pinning control in part of time interval. The topology of the networked system is assumed to be directed and weakly connected. The agents in each group can be classified into three subsets, which are inter-act agent, intra-act agent with zero in-degree and the other agents. According to the agents’ property and intrinsic dynamics, the protocol is designed to guarantee that agents in the same group reach consensus, and the agents in different groups reach group-delay consensus. By using Lyapunov stability theory, graph theory and matrix theory, some consensus criteria are derived in the form of matrix inequalities. At last, a numerical simulation is also given to verify the correctness of theoretical analysis.