Algebraic Riccati Equations

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Algebraic Riccati equations play a central role in modern control theory and signal processing, essential topics for industrial scientists, engineers, and mathematicians. This book provides a thorough treatment of the theory behind these equations, the solutions arising from continuous and discrete systems, and includes a collection of eight problem areas or applications in which they play a crucial role.

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Product Details

  • ISBN-13: 9780198537953
  • Publisher: Oxford University Press, USA
  • Publication date: 9/28/1995
  • Series: Oxford Mathematical Monographs
  • Pages: 504
  • Product dimensions: 6.44 (w) x 9.50 (h) x 1.27 (d)

Meet the Author

University of Calgary

College of William and Mary, Virginia

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Table of Contents

Pt. I Matrix Theory 1
1 Preliminaries from the Theory of Matrices
2 Indefinite Scalar Products
3 Skew-Symmetric Scalar Products
4 Matrix Theory and Control
5 Linear Matrix Equations
6 Rational Matrix Functions
Pt. II Continuous Algebraic Riccati Equations 147
7 Geometric Theory: The Complex Case
8 Geometric Theory: The Real Case
9 Constructive Existence and Comparison Theorems
10 Hermitian Solutions and Factorizations of Rational Matrix Functions
11 Perturbation Theory
Pt. III Discrete Algebraic Riccati Equations 269
12 Geometric Theory for the Discrete Algebraic Riccati Equation
13 Constructive Existence and Comparison Theorems
14 Perturbation Theory for Discrete Algebraic Riccati Equations
15 Discrete Algebraic Riccati Equations and Matrix Pencils
Pt. IV Applications and Connections 347
16 Linear-Quadratic Regulator Problems
17 The Discrete Kalman Filter
18 The Total Least Squares Technique
19 Canonical Factorization
20 [actual symbol not reproducible] Control Problems
21 Contractive Rational Matrix Functions
22 The Matrix Sign Function
23 Structured Stability Radius
Bibliography 459
List of Notation and Conventions 473
Index 477
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