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 HW*w control and total least squares methods.

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

Peter Lancaster , Department of Mathematics and Statistics, University of Calgary, Leiba Rodman , Department of Mathematics, College of William and Mary, Virginia