Curtain, Ruth - ed. ; Kaashoek, Rien - ed.
Infinite-Dimensional Systems Theory and Operator Theory
The following is a short survey of the notion of a well-posed linear system. We start by describing the most basic concepts, proceed to discuss dissipative and conservative systems, and finally introduce J-energy-preserving systems, i.e., systems that preserve energy with respect to some generalized inner products (possibly semi-definite or indefinite) in the input, state and output spaces. ; The class of well-posed linear systems contains most linear time-independent distributed parameter systems: internal or boundary control of PDE's, integral equations, delay equations, etc. These systems have existed in an implicit form in the mathematics literature for a long time, and they are closely connected to the scattering theory by Lax and Phillips and to the model theory by Sz.-Nagy and Foiaş. ; The theory has been developed independently by many different schools, and it is only recently that these different approaches have begun to converge. One of the most interesting objects of the present study is the Riccati equation theory for this class of infinite-dimensional systems.
Zielona Góra: Uniwersytet Zielonogórski
AMCS, volume 11, number 6 (2001) ; click here to follow the link
Biblioteka Uniwersytetu Zielonogórskiego
Sep 3, 2021
Jul 22, 2021
64
https://zbc.uz.zgora.pl/publication/65603
Edition name | Date |
---|---|
J-energy preserving well-posed linear systems | Sep 3, 2021 |
Weiss, George Staffans, Olof J. Tucsnak, Marius Fliess, Michel - ed. Jai, Abdelhaq El - ed.
Błachuta, Marian J. Kowalczuk, Zdzisław - red.
Pandolfi, Luciano Curtain, Ruth - ed. Kaashoek, Rien - ed.
Liu, Pin-Lin Korbicz, Józef - red. Uciński, Dariusz - red.
Li, Jing-Rebecca White, Jacob Campbell, Stephen L. - ed.
Karelin, Irina Lerer, Leonid Curtain, Ruth - ed. Kaashoek, Rien - ed.
Janiszowski, Krzysztof B. Korbicz, Józef - red. Uciński, Dariusz - red.
Dym, Harry Fliess, Michel - ed. Jai, Abdelhaq El - ed.