Boundary control systems in factor form: Transfer functions and input-output maps

Integral Equations and Operator Theory

Volumn 41, Issue 1, 2001, Pages 1-37

  Grabowski, Piotr ^a   Callier, Frank M ^b  

^a AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

^b UNIVERSITY OF NAMUR   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012457743     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01202529     Document Type: Article

References (31)

1. H.BATEMAN, A.ERDÉLYI, V.MAGNUS, F. OBERHETTINGER, F.TRICOMI, Tables of Integral Transforms. vol. I, New York: McGraw - Hill, 1954.
2. F.M.CALLIER, C. A.DESOER, An algebra of transfer functions of distributed linear time-invariant systems, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 25 (1978), pp. 651-662; correction, ibidem, 26 (1979), p. 360.
3. F.M.CALLIER, J.WINKIN, Infinite dimensional system transfer functions, in Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems, R. F.CURTAIN, A.BENSOUSSAN AND J.L.LIONS (Eds.), Berlin: Springer, LECTURE NOTES in CONTROL and INFORMATION SCIENCES, 185 (1993), pp. 75-101.
4. J.B.CONWAY, Functions of One Complex Variable, New York: Springer, 1978.
5. R.F.CURTAIN, Well-posedness of infinite-dimensional linear systems in time and frequency domain, Systems and Control Group, Mathematics Institute, Research Report TW-287 (1988). University of Groningen, The Netherlands.
6. R.F.CURTAIN, Input-output stability and exponential stability of infinite-dimensional systems, MATHEMATICAL SYSTEMS THEORY, 21 (1988), pp. 19-48.
7. R.F.CURTAIN AND G.WEISS, Well-posedness of triple of operators (in the sense of linear systems theory). In: (Eds.) W.DESCH, F.KAPPEL AND K.KUNISCH, Estimation and Control of Distributed Parameter Systems. Proceedings of the International conference on Control and Estimation of Distributed Parameter Systems, Vorau, 1988. Birkhäuser: Basel, 1989. ISNM series vol. 91, pp. 41-59.
8. R.CURTAIN, H.ZWART, An Introduction to Infinite-Dimensional Linear Systems Theory, Heidelberg: Springer, 1995.
9. G.DOETSCH, Introduction to the Theory and Applications of the Laplace Transformation, Berlin: Springer, 1974.
10. P.FUHRMANN, Linear Systems and Operators in Hilbert space, New York: McGraw-Hill, 1981.
11. H.GÓRECKI, S.FUKSA, P.GRABOWSKI, A.KORYTOWSKI Analysis and Synthesis of Time-Delay Systems, Warsaw & Chichester: PWN and J.Wiley, 1989.
12. P.GRABOWSKI, On the spectral - Lyapunov approach to parametric optimization of distributed parameter systems, IMA JOURNAL of MATHEMATICAL CONTROL and INFORMATION, 7 (1990), pp. 317 - 338.
13. P.GRABOWSKI, The LQ controller problem: an example, IMA JOURNAL of MATHEMATICAl CONTROL and INFORMATION, 11 (1994), pp. 355-368.
14. P.GRABOWSKI, Admissibility of observation functionals, INTERNATIONAL JOURNAL of CONTROL, 62 (1995), pp. 1161-1173.
15. P.GRABOWSKI, F.M.CALLIER, Admissibility of observation operators. Semigroup criteria of admissibility, INTEGRAL EQUATIONS and OPERATOR THEORY, 25 (1996), pp. 183-196.
16. P.GRABOWSKI, F.M.CALLIER, Admissible observation operators. Duality of observation and control using factorizations, DYNAMICS of CONTINUOUS, DISCRETE and IMPULSIVE SYSTEMS, 6 (1999), pp. 87-119.
17. 2 Spaces, Berlin: Springer, 1978.
18. E. Hille, Analytic Function Theory. Volume II, Boston: Ginn, 1962.
19. K.HOFFMAN, Banach Spaces of Analytic Functions, Englewood Cliffs: Prentice - Hall, 1962.
20. I.LASIECKA, R.TRIGGIANI, Feedback semigroups and cosine operators for boundary feedback parabolic and hyperbolic equations, JOURNAL of DIFFERENTIAL EQUATIONS, 47 (1983), pp. 246-272.
21. I.LASIECKA, R.TRIGGIANI, Stabilization and structural assignment of Dirichlet boundary feedback parabolic equations, SIAM JOURNAL on CONTROL and OPTIMIZATION, 21 (1983) pp. 766-803.
22. I.LASIECKA, R.TRIGGIANI, Finite rank, relatively bounded perturbations of semigroups generators II. ANNALI di MATEMATICA PURA ed APPLICATA, CXLIII (1986), pp. 47-100.
23. J.G.KRZYŻ, Problems in Complex Variable Theory. New York: Elsevier, 1972.
24. A.PAZY, Semigroups of Linear Operators and Applications to PDEs, Heidelberg: Springer, 1983.
25. W.RUDIN, Real and Complex Analysis, New York: McGraw-Hill, 1974.
26. J.WEIDMANN, Linear Operators in Hilbert Spaces, Heidelberg: Springer, 1980.
27. G.WEISS, Admissible observation operators for linear semigroups, ISRAEL JOURNAL of MATHEMATICS, 65 (1989), pp.17-43.
28. G.WEISS, Transfer functions of regular linear systems. Part I: Characterization of regularity, TRANSACTIONS of the AMS, 342 (1994), pp. 827-854.
29. G.WEISS, Regular linear systems with feedback, MATHEMATICS of CONTROL SIGNALS and SYSTEMS, 7 (1994), pp. 23-57.
30. M.WEISS, G.WEISS, Optimal control of stable weakly regular linear systems, MATHEMATICS of CONTROL SIGNALS and SYSTEMS, 10 (1997), pp. 287-330.
31. A.H.ZEMANIAN, Distribution Theory and Transform Analysis, New York: McGraw-Hill, 1965.