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Exact observability of diagonal systems with a one-dimensional output operator

100%

Jacob B., Zwart H.

International Journal of Applied Mathematics and Computer Science

2001

tom 11

nr 6

1277-1283

In this paper equivalent conditions for exact observability of diagonal systems with a one-dimensional output operator are given. One of these equivalent conditions is the conjecture of Russell and Weiss (1994). The other conditions are given in terms of the eigenvalues and the Fourier coefficients of the system data.

J-energy preserving well-posed linear systems

58%

Staffans O. J.

International Journal of Applied Mathematics and Computer Science

2001

tom 11

nr 6

1361-1378

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).

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

1 Jacob B.

1 Staffans O. J.

1 Zwart H.

2 2001

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Exact observability of diagonal systems with a one-dimensional output operator

J-energy preserving well-posed linear systems