Sampled-Data Consensus of Networked Euler-Lagrange Systems: A Discrete Small-Gain Approach

This paper studies the sampled-data consensus of networked Euler-Lagrange systems. The sampled-data feedback causes infinities at sampling instants in the control input due to the differentiation of the feedback by the conventional control law designed for Euler-Lagrange systems. Although directly removing the differentiation term from the control law may completely avoid the infinity problem, the overall dynamics are also vastly altered. A problem with this method is that its Lyapunov function of the auxiliary variable may increase at sampling instants, making Lyapunov analysis unviable. To address this problem, the interactions between the auxiliary variable and the states are re- analyzed under the new control law, converting the sampled-data consensus problem into the stability of two interconnected subsystems of states and auxiliary variables, respectively. By a modified discrete small gain analysis, the subsystems are proved to be asymptotically stable under a discrete-time small-gain condition, and the consensus of the networked Euler-Lagrange Systems thus follows. It is shown that despite the individual Lyapunov functions for the states and auxiliary variables might not be strictly decreasing, consensus of the overall system is still guaranteed under the small-gain consensus condition.