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A Grassmanian approach to the Hankel norm approximation problem

Iftime, Orest; Kaashoek, Rien; Sandberg, Henrik LU and Sasane, Amol (2004) In Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS)
Abstract
This paper concerns the unifying framework to strictly contractive extension problems, which is usually referred to as the band method. The solution to the so-called strictly contractive extension problem in this abstract framework, when applied to a certain concrete case, yields a complete characterization of solutions to the sub-optimal Nehari problem. The sub-optimal Hankel norm approximation problem is a more general problem, which is closely related to the model reduction problem in control theory. It covers the Nehari problem as a special case, but does not fit into the existing abstract framework. This problem is addressed in the present paper. In this paper the Grassmannian version of the band method is suitable enlarged so as to... (More)
This paper concerns the unifying framework to strictly contractive extension problems, which is usually referred to as the band method. The solution to the so-called strictly contractive extension problem in this abstract framework, when applied to a certain concrete case, yields a complete characterization of solutions to the sub-optimal Nehari problem. The sub-optimal Hankel norm approximation problem is a more general problem, which is closely related to the model reduction problem in control theory. It covers the Nehari problem as a special case, but does not fit into the existing abstract framework. This problem is addressed in the present paper. In this paper the Grassmannian version of the band method is suitable enlarged so as to include the sub-optimal Hankel norm approximation problem as a special case as well. Our abstract result is illustrated on two concrete problems, one for time-invariant infinite dimensional systems and the other for time-variant periodic finite dimensional systems. (Less)
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Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS)
ISBN
90-5682-517-8
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7addacd5-8057-4c1a-aefb-843792f7f969 (old id 536050)
date added to LUP
2007-09-20 09:22:27
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@inproceedings{7addacd5-8057-4c1a-aefb-843792f7f969,
  abstract     = {This paper concerns the unifying framework to strictly contractive extension problems, which is usually referred to as the band method. The solution to the so-called strictly contractive extension problem in this abstract framework, when applied to a certain concrete case, yields a complete characterization of solutions to the sub-optimal Nehari problem. The sub-optimal Hankel norm approximation problem is a more general problem, which is closely related to the model reduction problem in control theory. It covers the Nehari problem as a special case, but does not fit into the existing abstract framework. This problem is addressed in the present paper. In this paper the Grassmannian version of the band method is suitable enlarged so as to include the sub-optimal Hankel norm approximation problem as a special case as well. Our abstract result is illustrated on two concrete problems, one for time-invariant infinite dimensional systems and the other for time-variant periodic finite dimensional systems.},
  author       = {Iftime, Orest and Kaashoek, Rien and Sandberg, Henrik and Sasane, Amol},
  booktitle    = {Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS)},
  isbn         = {90-5682-517-8},
  language     = {eng},
  title        = {A Grassmanian approach to the Hankel norm approximation problem},
  year         = {2004},
}