Distributed leader-tracking adaptive control for high-order nonlinear Lipschitz multi-agent systems with multiple time-varying communication delays

This paper addresses the leader-tracking problem of high-order nonlinear Lipschitz agents sharing their state information through a delayed communication network. The multiple delays associated to each communication link are considered as time-varying functions. The problem is solved through a fully distributed adaptive protocol on the basis of a node-based local adaptation method that is independent of any global information and does not require any knowledge or estimation of the nonlinear agent dynamics. The stability of the closed-loop delayed Multi-Agent System (MAS) is proven to leverage the Lyapunov–Krasovskii approach combined with the Barbalat's Lemma. Stability conditions are expressed as a set of feasible Linear Matrix Inequalities (LMIs) derived via the free weighted matrices method. Exemplary numerical simulations confirm the effectiveness of the theoretical results.