An operator theoretic approach to infinite‐dimensional control systems. Issue 4 (15th October 2018)

• Record Type: Journal Article
• Authors: Jacob, Birgit; Zwart, Hans
• Other Names: Jacob Birgit guestEditor.; Behrndt Jussi guestEditor.; Tretter Christiane guestEditor.; Trunk Carsten guestEditor.
• Is Part Of: Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik. Volume 41:Issue 4(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-10-15
• Subjects: C0‐semigroup -- infinite‐dimensional systems theory -- partial differential equation -- port‐Hamiltonian system -- stability -- stabilizability; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; 510.5
• DOI: 10.1002/gamm.201800010
• Languages: English
• ISSNs: 0936-7195

Abstract

Abstract : In this survey we use an operator theoretic approach to infinite‐dimensional systems theory. As this research field is quite rich, we restrict ourselves to the class of infinite‐dimensional linear port‐Hamiltonian systems and we will focus on topics such as well‐posedness, stability and stabilizability. We combine the abstract operator theoretic approach with the more physical approach based on Hamiltonians. This enables us to derive easy verifiable conditions for well‐posedness and stability.