A State Space Approach to Canonical Factorization with Applications

1. Introduction
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

Part I. Convolution equations, canonical factorization and the state space method

2. The role of canonical factorization in solving convolution equations
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

3. The state space method and factorization
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

Part II. Convolution equations with rational matrix symbols

4. Explicit solutions using realizations
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

5. Factorization of non-proper rational matrix functions
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

Part III. Equations with non-rational symbols

6. Factorization of matrix functions analytic in a strip
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

7. Convolution equations and the transport equation
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

8. Wiener-Hopf factorization and factorization indices
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

Part IV. Factorization of selfadjoint rational matrix functions

9. Preliminaries concerning minimal factorization
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

10. Factorization of positive definite rational matrix functions
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

11. Pseudo-spectral factorizations of selfadjoint rational matrix functions
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

12. Review of the theory of matrices in indefinite inner product spaces
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

Part V. Riccati equations and factorization

13. Canonical factorization and Riccati equations
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

14. The symmetric algebraic Riccati equation
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

15. J-spectral factorization
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

Part VI. Factorizations and symmetries

16. Factorization of positive real rational matrix functions
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

17. Contractive rational matrix functions
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

18. J-unitary rational matrix functions
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

Part VII. Applications of J-spectral factorizations

19. Application to the rational Nehari problem
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

20. Review of some control theory for linear systems
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

21. H-infinity control applications
Harm Bart, Marinus A. Kaashoek, André C. M. Ran

Keywords: Mathematics, Operator Theory, Linear and Multilinear Algebras, Matrix Theory, Operations Research, Mathematical Programming, Functions of a Complex Variable