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. H^oo control problems
21. Contractive rational matrix functions
22. The matrix sign function
23. Structured stability radius
Bibliography
List of notations
Index