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The Dissipation Inequality and the Algebraic Riccati Equation

  • Chapter
The Riccati Equation

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

Abstract

Undoubtedly one of the most important concepts in linear systems and control, both from a theoretical as well as from a practical point of view, is the algebraic Riccati equation. Since its introduction in control theory by Kaiman [16] the beginning of the sixties, the algebraic Riccati equation has known an impressive range of applications, such as linear quadratic optimal control, stability theory, stochastic filtering and stochastic control, stochastic realization theory, synthesis of linear passive networks, differential games and, most recently, H ∞ optimal control and robust stabilization. The purpose of the present paper is to give an expository survey of the main concepts, results and applications related to the algebraic Riccati equation.

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Authors
  1. H. L. Trentelman
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  2. Jan C. Willems
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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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Trentelman, H.L., Willems, J.C. (1991). The Dissipation Inequality and the Algebraic Riccati Equation. 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_8

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  • DOI: https://doi.org/10.1007/978-3-642-58223-3_8

  • 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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