On the internal realization of polynomial response maps / by Eduardo Daniel Sontag.

v CHAPTER I. OUTLINE OF MAIN CONTRIBUTIONS 1 II. ALGEBRAIC PRELIMINARIES l6 1. k-Reduced Algebras 1? 2. The Zariski Topology • 2^ 3. k-Spaces 9 k. Dimension • " 5i III. REALIZATION THEORY ^rd hP 5. Volterra Series Ht 6. Construction of ft and I 50 7. Abstract Response Maps and Systems 54 8. Polynomial Response Maps and k-Systems 60 9. Quasi-Reachability ^2 10. Algebraic Observability °3 11. Existence and Uniqueness of Canonical Realizations . 67 IV. FINITENESS CONDITIONS * * ^ 12. The Observables of f ^9 13. Finite Realizability and Minimality ......... 75 1U. Polynomial Canonical Systems 77 15. Bounded Maps 16. Input/Output Equations °5 17. Jacobian Condition °^ 18. Some Examples and Counterexamples 9 1 V. STATE-AFFINE SYSTEMS 101 19. Recognizable Series ^ 20. State-Affine Systems ^5 21. Finite Response Maps and Cascades of Linear Systems . 109 22. Rationality m