Stability of an Euler-Bernoulli beam with a nonlinear dynamic feedback system
Analysis of PDEs
2015-10-21 v2
Abstract
This paper is concerned with the stability analysis of a lossless Euler-Bernoulli beam that carries a tip payload which is coupled to a nonlinear dynamic feedback system. This setup comprises nonlinear dynamic boundary controllers satisfying the nonlinear KYP lemma as well as the interaction with a nonlinear passive environment. Global-in-time wellposedness and asymptotic stability is rigorously proven for the resulting closed-loop PDE-ODE system. The analysis is based on semigroup theory for the corresponding first order evolution problem. For the large-time analysis, precompactness of the trajectories is shown by deriving uniform-in-time bounds on the solution and its time derivatives.
Cite
@article{arxiv.1505.07576,
title = {Stability of an Euler-Bernoulli beam with a nonlinear dynamic feedback system},
author = {Maja Miletić and Dominik Stürzer and Anton Arnold and Andreas Kugi},
journal= {arXiv preprint arXiv:1505.07576},
year = {2015}
}