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An operator theoretic approach to infinite‐dimensional control systems
Author(s) -
Jacob Birgit,
Zwart Hans
Publication year - 2018
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201800010
Subject(s) - verifiable secret sharing , operator (biology) , hamiltonian (control theory) , class (philosophy) , hamiltonian system , focus (optics) , mathematics , stability (learning theory) , port (circuit theory) , computer science , calculus (dental) , algebra over a field , pure mathematics , mathematical optimization , mathematical analysis , physics , engineering , artificial intelligence , dentistry , repressor , chemistry , optics , biochemistry , machine learning , transcription factor , programming language , medicine , set (abstract data type) , electrical engineering , gene
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.