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Explicit formulae for J-spectral factors for regular linear systems

By R. F. Curtain and Amol Sasane

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

Topics: QA Mathematics
Year: 2002
OAI identifier: oai:eprints.lse.ac.uk:9735
Provided by: LSE Research Online
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