Algebraic Riccati Equations

Hardcover | July 1, 1995

byPeter Lancaster, Leiba Rodman

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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 andrational 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 excitingcollection 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 HO*w control and total least squares methods.

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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 andrational matrix functions. The second and t...

P. Lancaster is at University of Calgary. L. Rodman is at College of William and Mary, Virginia.

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Format:HardcoverDimensions:498 pages, 9.21 × 6.14 × 1.26 inPublished:July 1, 1995Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198537956

ISBN - 13:9780198537953

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Table of Contents

1. Preliminaries from the theory of matrices2. Indefinite scalar products3. Skew-symmetric scalar products4. Matrix theory and control5. Linear matrix equations6. Rational matrix functions7. Geometric theory: the complex case8. Geometric theory: the real case9. Constructive existence and comparison theorems10. Hermitian solutions and factorizations of rational matrix functions11. Perturbation theory12. Geometric theory for the discrete algebraic Riccati equation13. Constructive existence and comparison theorems14. Perturbation theory for discrete algebraic Riccati equations15. Discrete algebraic Riccati equations and matrix pencils16. Linear-quadratic regulator problems17. The discrete Kalman filter18. The total least squares technique19. Canonical factorization20. Hoo control problems21. Contractive rational matrix functions22. The matrix sign function23. Structured stability radiusBibliographyList of notationsIndex

Editorial Reviews

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