Leader-following consensus with disturbance rejection for uncertain Euler-Lagrange systems over switching networks

In this paper, the leader-following consensus with disturbance rejection problem of uncertain Euler-Lagrange systems is studied by the adaptive distributed observer approach. We first present a key lemma that guarantees the existence of an exponentially convergent adaptive distributed observer for linear leader systems without exponential growing modes over jointly connected switching and directed communication networks. This lemma also provides a specific Lyapunov function for the error dynamics of the adaptive distributed observer, which will play a crucial role in establishing one of the main results. A special case of this result where there is no disturbance will extend the existing result for a neutrally stable leader system and undirected communication networks to the case where the communication networks are directed and the leader's positional signal includes the class of ramp signals. Two examples will be given to demonstrate the effectiveness of the new results.