2015/05/28 by Maja Miletić, Miletić, Maja, Dominik Stürzer +5
Engineering · Mathematics · #35B35 #35Q93 #93D15 #93D20 #Analysis of PDEs (math.AP) #Control and Stability of Dynamical Systems #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Stability and Controllability of Differential Equations #math.AP #msc:35B35 #msc:35Q93 #msc:93D15 #msc:93D20
paper · pdf · doi:10.48550/arxiv.1505.07576
openalex publication_date 2015/05/28 · arxiv created 2015/10/20 · arxiv updated 2015/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.