Strict Lyapunov-Krasovskii Functionals for undirected networks of Euler-Lagrange systems with time-varying delays

For an undirected network of nonidentical interconnected Euler-Lagrange systems whose communication is affected by varying time-delays that may not be differentiable, we consider the problem of establishing leaderless and leader-follower consensus via the simplest Proportional plus damping decentralized controller. The main contribution of this work is to prove that the agents' positions and velocities converge uniformly, globally, and asymptotically to a common non-specified position in the leaderless case, and to a given reference in the leader-follower case. The main results are established via Lyapunov's direct method; a Strict Lyapunov-Krasovskii Functional is constructed, to the best of our knowledge, for the first time in the literature. It is shown that the resulting closed-loop system is Input-to-State Stable with regards to external additive inputs (perturbations). In turn, the separation principle applies to a certainty-equivalence controller, implemented with any globally convergent velocity estimator, such as the Immersion and Invariance observer. (C) 2019 Elsevier B.V. All rights reserved.