期刊名称：International Journal of Applied Mathematics and Computer Science
电子版ISSN：2083-8492
出版年度：2001
卷号：11
期号：6
出版社：De Gruyter Open
摘要：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 ( H2 - and H∞ -theories).
关键词：well-posed linear system; system node; transfer function; Lax-Phillips semigroup; dissipative system; conservative system; model theory; conservative realization; J -energy-preserving system; Lyapunov equation; Riccati equation
