Strict Lyapunov–Krasovskiĭ Functionals for undirected networks of Euler–Lagrange systems with time-varying delays
Résumé
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-Krasovskiı̆ 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 & Invariance observer.
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