Weak admissibility does not imply admissibility for analytic semigroups

Systems and Control Letters

Volumn 48, Issue 3-4, 2003, Pages 341-350

  Zwart, Hans ^a   Jacob, Birgit ^b   Staffans, Olof ^c  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b TU DORTMUND UNIVERSITY   (Germany)

^c ÅBO AKADEMI UNIVERSITY   (Finland)

Author keywords

Admissible control operator; C0 semigroup; Conditional basis; Infinite dimensional system

Indexed keywords

BOUNDARY CONDITIONS; LINEAR EQUATIONS; THEOREM PROVING; VECTORS;

CONTROL OPERATORS;

CONTROL SYSTEMS;

EID: 0037445052     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(02)00277-3     Document Type: Article

References (18)

1. Benamara N.-E., Nikolski N. Resolvent test for similarity to a normal operator. Proc. London Math. Soc. 78:1999;585-626.
2. R.F. Curtain, H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, Texts in Applied Mathematics, Vol. 21, Springer, New York, 1995.
3. Engel K.-J. On the characterization of admissible control- and observation operators. Systems Control Lett. 34:1998;225-227.
4. Garnett J.B. Bounded Analytic Functions. 1981;Academic Press, New York.
5. Grabowski P., Callier F.M. Admissible observation operators, semigroup criteria of admissibility. Integral Equation Oper. Theory. 25:1996;182-198.
6. 2 Systems Control Lett. 16:1991;219-227.
7. Ho L.F., Russell D.L. Admissible input elements for systems in Hilbert space and a Carleson measure criterion. SIAM J. Control Optim. 21(4):1983;614-640.
8. B. Jacob, J.R. Partington, S. Pott, Admissible and weakly admissible observation operators for the right shift semigroup, Proc. Edinburgh Math. Soc. (2) 45 (2) (2002) 353-362.
9. I. Lasiecka, R. Triggiani, Control Theory for Partial Differential Equations: Continuous and Approximation Theories, Vols. I-II, Cambridge University Press, Cambridge, 2000.
10. Le Merdy C. A bounded compact semigroup on Hilbert space not similar to a contraction one. Progr. Nonlinear Differential Equations Appl. 42:2000;213-216.
11. C. Le Merdy, The Weiss conjecture for bounded analytic semigroups, J. London Math. Soc., to appear.
12. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. 1983;Springer, New York.
13. Salamon D. Infinite dimensional linear systems with unbounded control and observation. a functional analysis approach Trans. Amer. Math. Soc. 300(2):1987;383-431.
14. Singer I. Bases in Banach Spaces I. 1970;Springer, Berlin.
15. O.J. Staffans, Well-Posed Linear Systems, Book manuscript (available at http://www.abo.fi/̃staffans).
16. 2 Systems Control Lett. 10:1988;79-82.
17. Weiss G. Admissibility of unbounded control operators. SIAM J. Control Optim. 27:1989;527-545.
18. Weiss G. Two conjectures on the admissibility of control operators. Desch W., Kappel F., Kunisch K. Estimation and Control of Distributed Parameter Systems. 1991;367-378 Birkhäuser, Basel.