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Algebraic Riccati Equation: Hermitian and Definite Solutions

  • Chapter
The Riccati Equation

Part of the book series: Communications and Control Engineering Series ((CCE))

Abstract

Let A, B, and C be constant n × n matrices with entries in C, the field of complex numbers. Let B and C be hermitian, i.e., B = B* and C = C*, where an asterisk is used to denote the conjugate transpose of a matrix. The quadratic equation

$$XA + A*X - XBX + C = 0$$
(3.1)

for the n × n complex matrix X is called the algebraic Riccati equation.

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Authors
  1. Vladimír Kučera
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Editor information

Editors and Affiliations

  1. Dipartimento di Elettronica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy

    Sergio Bittanti

  2. Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, 93106, USA

    Alan J. Laub

  3. Department of Mathematics, University of Groningen, P.O. Box 800, NL-9700 AV, Groningen, The Netherlands

    Jan C. Willems

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© 1991 Springer-Verlag Berlin Heidelberg

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Kučera, V. (1991). Algebraic Riccati Equation: Hermitian and Definite Solutions. In: Bittanti, S., Laub, A.J., Willems, J.C. (eds) The Riccati Equation. Communications and Control Engineering Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58223-3_3

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  • DOI: https://doi.org/10.1007/978-3-642-58223-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63508-3

  • Online ISBN: 978-3-642-58223-3

  • eBook Packages: Springer Book Archive

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