Properties of the realization of inner functions

Mathematics of Control, Signals, and Systems

Volumn 15, Issue 4, 2002, Pages 356-379

  Jacob, Birgit ^a   Zwart, Hans ^b  

^a TU DORTMUND UNIVERSITY   (Germany)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Exponential stability; Infinite dimensional systems; Inner functions; Realization theory; Semigroups of operators

Indexed keywords

BOUNDARY CONDITIONS; FUNCTION EVALUATION; INVERSE PROBLEMS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; SYSTEM STABILITY; TRANSFER FUNCTIONS;

BLASCHKE PRODUCT; CARLESON-NEWMAN CONDITION; EXPONENTIAL STABILITY; INFINITE DIMENSIONAL SYSTEMS; INNER FUNCTIONS; REALIZATION THEORY;

STATE SPACE METHODS;

EID: 0036934852     PISSN: 09324194     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004980200015     Document Type: Article

References (25)

1. 2-functions and infinite-dimensional realization theory. SIAM J. Control, 13:221-241, 1973.
2. R. F. Curtain and G. Weiss. Well-posedness of triples of operators (in the sense of linear systems theory). In W. Schappacher, F. Kappel, K, Kunisch, editors, Distributed Parameter Systems (proceedings of the conference in Vorau, Austria, July 1988), pages 41-59; Birkhäuser Verlag, Basel, 1989.
3. p Spaces. Number 38 in Pure and Applied Mathematics. Academic Press, San Diego, CA, 1970.
4. P. A. Fuhrmann. Linear Systems and Operators in Hilbert Space. McGraw-Hill, New York, 1981.
5. J. B. Garnett. Bounded Analytic Functions. Academic Press, New York, 1981.
6. L. Gearhart. Spectral theory for contraction semigroups on Hilbert space. Trans. Amer. Math. Soc., 236:385-394, 1978.
7. J. W. Helton. Systems with infinite-dimensional state-space: the Hilbert space approach. Proc. IEEE, 64:145-160, 1976.
8. K. Hoffman. Banach Spaces of Analytic Functions. Prentice-Hall, Englewood Cliffs, NJ, 1962.
9. B. Jacob and H. Zwart, Equivalent conditions for stabilizability of infinite-dimensional systems with admissible control operators. SIAM J. Control Optim., 37(5):1419-1455, 1999.
10. 0-groups with one-dimensional input operators. In F. Colonius, U. Helmke, D. Prätzel-Walters, F. Wirth, editors, Advances in Mathematical Systems Theory (a volume in honor of Diederich Hinrichsen), pages 221-242, Systems Control Found. Appl., Birkhäuser Boston, Boston, MA, 2001.
11. B. Jacob and H. Zwart, Review on realization theory for infinite-dimensional systems. Available at http:\www.math.utwente.nl~twhans.
12. J. W. Moeller. On the spectra of some translation spaces. J. Math. Anal. Appl., 4:276-296, 1962.
13. N. K. Nikolskii. Treatise on the Shift Operator. Springer-Verlag, Berlin, 1986.
14. R. J. Ober and Y. Wu. Infinite-dimensional continuous-time linear systems: stability and structure analysis. SIAM J. Control Optim., 34(3):757-812, 1996.
15. M. Rosenblum and J. Rovnyak, Hardy Classes and Operator Theory. Oxford University Press, New York, 1985.
16. D. Salamon. Realization theory in Hilbert space. Math. Systems Theory, 21:147-164, 1989.
17. G. Weiss. Admissibility of unbounded control operators. SIAM J. Control Optim., 27:527-545, 1989.
18. G. Weiss. Admissible observation operators for linear semigroups. Israel J. Math., 65:17-43, 1989.
19. G. Weiss. The representation of regular linear systems on Hilbert spaces. In W. Schappacher, F. Kappel, K. Kunisch, editors, Distributed Parameter Systems (proceedings of the conference in Vorau, Austria, July 1988), pages 401-416. Birkhäuser Verlag, Basel, 1989.
20. G. Weiss. Regular linear systems with feedback. Math. Control Signals Systems, 7:23-57, 1994.
21. G. Weiss. Transfer functions of regular linear systems, part I: characterizations of regularity. Trans. Amer. Math. Soc., 342:827-854, 1994.
22. Y. Yamamoto. Realization theory of infinite-dimensional linear systems, part I. Math. Systems Theory, 15:55-77, 1981.
23. Y. Yamamoto. Realization theory of infinite-dimensional linear systems, part II. Math. Systems Theory, 15:169-190, 1982.
24. Y. Yamamoto. Equivalence of internal and external stability for a class a distributed systems. Math. Control Signals Systems, 4:391-409, 1991.
25. H. Zwart, Y. Yamamoto and Y. Gotoh. Stability is realization-dependent: some examples. Systems Control Lett., 24:25-31, 1995.