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J-Symmetric Factorizations and Algebraic Riccati Equations

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Recent Advances in Operator Theory

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 124))

Abstract

This paper discusses two interrelated topics: minimal J-symmetric factorizations of rational matrix functions and the algebraic Riccati equation. In particular, necessary and sufficient conditions are presented for the existence of a complete set of minimal J-symmetric factorizations of a selfadjoint rational matrix function with constant signature. For the algebraic Riccati equation the selfadjoint function which is of vital importance is the Popov function. Our first result for the algebraic Riccati equation describes the connection between the hermitian solutions, J-symmetric factorizations of the Popov function and generalized Bezoutians. Then, necessary and sufficient conditions are given for the algebraic Riccati equation to have a complete set of solutions. Both the continuous and discrete algebraic Riccati equation are treated.

Dedicated to Israel Gohberg on the occasion of his seventieth birthday with admiration and affection

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Author information

Authors and Affiliations

  1. Technion Israel Institute of Technology, Department of Mathematics, Haifa, 32000, Israel

    I. Karelin & L. Lerer

  2. Divisie Wiskunde en Informatica, Faculteit Exacte Wetenschappen Vrije Universiteit, de Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    A. C. M. Ran

Authors
  1. I. Karelin
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  2. L. Lerer
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  3. A. C. M. Ran
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    A. Dijksma

  2. Division of Mathematics and Computer Science Faculty of Sciences, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek  & A. C. M. Ran  & 

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© 2001 Springer Basel AG

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Karelin, I., Lerer, L., Ran, A.C.M. (2001). J-Symmetric Factorizations and Algebraic Riccati Equations. In: Dijksma, A., Kaashoek, M.A., Ran, A.C.M. (eds) Recent Advances in Operator Theory. Operator Theory: Advances and Applications, vol 124. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8323-8_16

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  • DOI: https://doi.org/10.1007/978-3-0348-8323-8_16

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9516-3

  • Online ISBN: 978-3-0348-8323-8

  • eBook Packages: Springer Book Archive

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