Consensus of a class of second-order nonlinear heterogeneous multi-agent systems with uncertainty and communication delay

In this paper, a consensus problem is studied for a group of second-order nonlinear heterogeneous agents with non-uniform time delay in communication links and uncertainty in agent dynamics. We design a class of novel decentralized control protocols for the consensus problem whose solvability is converted into stability analysis of an associated closed-loop system with uncertainty and time delay. Using an explicitly constructed Lyapunov functional, the stability conditions or the solvability conditions of the consensus problem are given in terms of a set of linear matrix inequalities apart from a small number of scalar parameters that appear nonlinearly. Furthermore, the linear matrix inequalities are theoretically verified to be solvable when the communication delay is sufficiently small. The effectiveness of the proposed control protocol is illustrated by numerical examples. Copyright (c) 2016 John Wiley & Sons, Ltd.