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The Riccati Equation

  • Book
  • © 1991

Overview

Editors:
  1. Sergio Bittanti

    1. Dipartimento di Elettronica, Politecnico di Milano, Milano, Italy

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  2. Alan J. Laub

    1. Department of Electrical and Computer Engineering, University of California, Santa Barbara, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Jan C. Willems

    1. Department of Mathematics, University of Groningen, Groningen, The Netherlands

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

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-X
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  2. Count Riccati and the Early Days of the Riccati Equation

    • Sergio Bittanti
    Pages 1-10

  3. Solutions of the Continuous and Discrete Time Algebraic Riccati Equations: A Review

    • Peter Lancaster, Leiba Rodman
    Pages 11-51

  4. Algebraic Riccati Equation: Hermitian and Definite Solutions

    • Vladimír Kučera
    Pages 53-88

  5. A Geometric View of the Matrix Riccati Equation

    • Mark A. Shayman
    Pages 89-112

  6. The Geometry of the Matrix Riccati Equation and Associated Eigenvalue Methods

    • Clyde F. Martin, Gregory Ammar
    Pages 113-126

  7. The Periodic Riccati Equation

    • Sergio Bittanti, Patrizio Colaneri, Giuseppe De Nicolao
    Pages 127-162

  8. Invariant Subspace Methods for the Numerical Solution of Riccati Equations

    • Alan J. Laub
    Pages 163-196

  9. The Dissipation Inequality and the Algebraic Riccati Equation

    • H. L. Trentelman, Jan C. Willems
    Pages 197-242

  10. The Infinite Horizon and the Receding Horizon LQ-Problems with Partial Stabilization Constraints

    • Jacques L. Willems, Frank M. Callier
    Pages 243-262

  11. Riccati Difference and Differential Equations: Convergence, Monotonicity and Stability

    • Robert R. Bitmead, Michel Gevers
    Pages 263-291

  12. Generalized Riccati Equations in Dynamic Games

    • Tamer Başar
    Pages 293-333

  13. Back Matter

    Pages 335-338
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Keywords

About this book

Conceived by Count Jacopo Francesco Riccati more than a quarter of a millennium ago, the Riccati equation has been widely studied in the subsequent centuries. Since its introduction in control theory in the sixties, the matrix Riccati equation has known an impressive range of applications, such as optimal control, H? optimization and robust stabilization, stochastic realization, synthesis of linear passive networks, to name but a few. This book consists of 11 chapters surveying the main concepts and results related to the matrix Riccati equation, both in continuous and discrete time. Theory, applications and numerical algorithms are extensively presented in an expository way. As a foreword, the history and prehistory of the Riccati equation is concisely presented.

Editors and Affiliations

  • Dipartimento di Elettronica, Politecnico di Milano, Milano, Italy

    Sergio Bittanti

  • Department of Electrical and Computer Engineering, University of California, Santa Barbara, USA

    Alan J. Laub

  • Department of Mathematics, University of Groningen, Groningen, The Netherlands

    Jan C. Willems

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