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Explicit formulae for J-spectral factors for regular linear systems

Curtain, R. F. and Sasane, Amol (2002) Explicit formulae for J-spectral factors for regular linear systems. In: Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems, 2002-08-12 - 2002-08-16. (Submitted)

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Abstract

The standard way to obtain explicit formulas for spectral factorization problems for rational transfer functions is to use a minimal realization and then obtain formulae in terms of the generators A, B, C and D. For well-posed linear systems with unbounded generators these formulae will not always be well-defined. Instead, we suggest another approach for the class of well-posed linear systems for which zero is in the resolvent set of A. Such a system is related to a reciprocal system having bounded generating operators depending on B, C, D and the inverse of A. There are nice connections between well-posed linear systems and their reciprocal systems which allow us to translate a factorization problem for the well-posed linear system into one for its reciprocal system, the latter having bounded generating operators. We illustrate this general approach by giving explicit solutions to the sub-optimal Nehari problem.

Item Type: Conference or Workshop Item (Paper)
Official URL: http://www.nd.edu/~mtns/
Additional Information: © 2002 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 07 Feb 2012 16:54
Last Modified: 11 Jun 2019 23:11
URI: http://eprints.lse.ac.uk/id/eprint/9735

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