Consensus in discrete-time one-sided Lipschitz nonlinear multi-agent systems with time-varying communication delay

Abstract

This paper discusses consensus in discrete-time nonlinear multi-agent systems with time-varying delay in a directed communication topology. Since each agent can obtain information only from its neighbouring agents, for the purpose of analysis, a consensus protocol is proposed that considers the relative position information between the leader and followers and between neighbouring followers under time-varying communication delay. This nonlinear problem is solved by employing nonlinear behaviour based on the one-sided Lipschitz method. By constructing an appropriate Lyapunov-Krasovskii function, the consensus criterion for the leader-following problem is established in terms of the linear matrix inequality (LMI) framework. Furthermore, the solution of gain matrix is addressed by utilizing the cone complementarity linearization (CCL) algorithm. The results of a numerical simulation indicate that this method can be used to effectively solve this problem.