An extension of Barbalat’s lemma with its application to synchronization of a class of switched networked nonlinear systems

This paper investigates the leader-following synchronization problem of uncertain Euler-Lagrange multi-agent systems subject to communication delays, disturbances and uniformly connected switching networks. The current settings cause great challenges to the solvability of the problem. To tackle these technical challenges, we make an extension to Barbalat’s lemma. Based on the certainty equivalence principle, we propose a novel adaptive distributed control law and apply the generalized Barbalat’s lemma to the synchronization problem. The effectiveness of the main result is demonstrated by an application to synchronization control of practical multiple mechanical systems.