Overview

This book provides a careful treatment of the theory of algebraic Riccati equations. It consists of four parts: the first part is a comprehensive account of necessary background material in matrix theory including careful accounts of recent developments involving indefinite scalar products and rational matrix functions. The second and third parts form the core of the book and concern the solutions of algebraic Riccati equations arising from continuous and discrete systems. The geometric theory and iterative analysis are both developed in detail. The last part of the book is an exciting collection of eight problem areas in which algebraic Riccati equations play a crucial role. These applications range from introductions to the classical linear quadratic regulator problems and the discrete Kalman filter to modern developments in HD*W*w control and total least squares methods.

Full Product Details

Author:   Peter Lancaster (Department of Mathematics and Statistics, Department of Mathematics and Statistics, University of Calgary) ,  Leiba Rodman (Department of Mathematics, Department of Mathematics, College of William and Mary, Virginia)
Publisher:   Oxford University Press
Imprint:   Clarendon Press
Dimensions:   Width: 16.30cm , Height: 3.20cm , Length: 24.20cm
Weight:   0.889kg
ISBN:  

9780198537953

ISBN 10:   0198537956
Pages:   498
Publication Date:   07 September 1995
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
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Table of Contents

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; 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; 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; 16. Linear-quadratic regulator problems; 17. The discrete Kalman filter; 18. The total least squares technique; 19. Canonical factorization; 20. Hoo control problems; 21. Contractive rational matrix functions; 22. The matrix sign function; 23. Structured stability radius; Bibliography; List of notations; Index

Reviews

""[T]his is a very useful book, both for pure and applied mathematicians and for electrical and control engineers."" --Mathematical Reviews

[T]his is a very useful book, both for pure and applied mathematicians and for electrical and control engineers. --Mathematical Reviews

[T]his is a very useful book, both for pure and applied mathematicians and for electrical and control engineers. --Mathematical Reviews<br>

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