Algebraic Riccati Equations

Abstract

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