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2001 | 11 | 6 | 1361-1378
Tytuł artykułu

J-energy preserving well-posed linear systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 (H^2 - and H^∞ -theories).
Rocznik
Tom
11
Numer
6
Strony
1361-1378
Opis fizyczny
Daty
wydano
2001
Twórcy
  • Department of Mathematics, Abo Akademi University, FIN-20500 Abo, Finland
Bibliografia
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Typ dokumentu
Bibliografia
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