Geodesic
J-energy preserving well-posed linear systems
International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 6, pp. 1361-1378.

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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 Foias. 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 Hinfty-theories).
Keywords: well-posed linear systems, system node, transfer function, Lax-Phillips semigroup, dissipative systems, conservative system, model theory, conservative realization, J-energy-preserving system, Lyapunov equations, Riccati equation
Mots-clés : układ zachowawczy, system liniowy, równanie Lyapunova, równanie różniczkowe Riccatiego 
@article{IJAMCS_2001_11_6_a7,
     author = {Staffans, O. J.},
     title = {J-energy preserving well-posed linear systems},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {1361--1378},
     publisher = {mathdoc},
     volume = {11},
     number = {6},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2001_11_6_a7/}
}
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Staffans, O. J. J-energy preserving well-posed linear systems. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 6, pp. 1361-1378. http://geodesic.mathdoc.fr/item/IJAMCS_2001_11_6_a7/