2021/06/21 by Rainer Picard, Picard, Rainer, Sascha Trostorff +5 · 1 citation
Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #Control and Stability of Dynamical Systems #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2106.10937
openalex publication_date 2021/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study port-Hamiltonian systems on a familiy of intervals and characterise all boundary conditions leading to m-accretive realisations of the port-Hamiltonian operator and thus to generators of contractive semigroups. The proofs are based on a structural observation that the port-Hamiltonian operator can be transformed to the derivative on a familiy of reference intervals by suitable congruence relations allowing for studying the simpler case of a transport equation. Moreover, we provide well-posedness results for associated control problems without assuming any additional regularity of the operators involved.