Consensus of a class of second-order nonlinear heterogeneous multi-agent systems with uniform time delay

In this paper, a consensus problem is studied for a group of second-order nonlinear heterogeneous agents with 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, stability conditions and solvability conditions of the consensus problem are given in terms of a set of linear matrix inequalities (LMIs) apart from a small number of scalar parameters that appear nonlinearly. The effectiveness of the proposed control protocol is illustrated by numerical examples.