Regularity of a Schrödinger equation with Dirichlet control and colocated observation

Systems and Control Letters

Volumn 54, Issue 11, 2005, Pages 1135-1142

  Guo, Bao Zhu ^a,b   Shao, Zhi Chao ^a,c  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

^b UNIVERSITY OF THE WITWATERSRAND   (South Africa)

^c UNIVERSITY OF CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Schr dinger equation; Transfer function; Well posed and regular system

Indexed keywords

CONTROL SYSTEMS; MATHEMATICAL OPERATORS; TRANSFER FUNCTIONS;

COLOCATED OBSERVATIONS; DIRICHLET CONTROL; SCHRÖDINGER EQUATION; WELL-POSED AND REGULAR FUNCTIONS;

WAVE EQUATIONS;

EID: 24944456252     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2005.04.008     Document Type: Article

References (25)

1. K. Ammari Dirichlet boundary stabilization of the wave equation Asymptotic Anal. 30 2002 117 130
2. K. Ammari, and M. Tucsnak Stabilization of second-order evolution equations by a class of unbounded feedbacks ESAIM Control Optim. Calc. Var. 6 2001 361 386
3. G. Avalos, I. Lasiecka, and R. Rebarber Lack of time-delay robustness for stabilization of a structural acoustics model SIAM J. Control Optim. 37 1999 1394 1418
4. G. Avalos, I. Lasiecka, and R. Rebarber Well-posedness of a structural acoustics model with point observation of the pressure J. Differential Equations 73 2001 40 78
5. C.I. Byrnes, D.S. Gilliam, V.I. Shubov, and G. Weiss Regular linear systems governed by a boundary controlled heat equation J. Dynam. Control Systems 8 2002 341 370
6. A. Cheng, and K. Morris Well-posedness of boundary control systems SIAM J. Control Optim 42 2003 1244 1265
7. R.F. Curtain The Salamon-Weiss class of well-posed infinite dimensional linear systems: a survey IMA J. Math. Control Inform. 14 1997 207 223
8. R.F. Curtain Linear operator inequalities for strongly stable weakly regular linear systems Math. Control, Signals, Systems 14 2001 299 337
9. R.F. Curtain, G. Weiss, Well-posedness of triples of operators (in the sense of linear systems theory), in: F. Kappel, K. Kunisch, W. Schappacher (Eds.), Control and Estimation of Distributed Parameter Systems, vol. 91, Birkhäuser, Basel, 1989, pp. 41-59.
10. B.Z. Guo, and Y.H. Luo Controllability and stability of a second-order hyperbolic system with colocated sensor/actuator Systems Control Lett. 46 2002 45 65
11. B.Z. Guo, K.M. Phung, X. Zhang, On the regularity of wave equation with partial Dirichlet control and observation, Academy of Mathematics and System Sciences, Academia Sinica, Beijing, China, 2004, preprint
12. V. Komornik Exact Controllability and Stabilization: The Multiplier Method 1994 Wiley Chichester
13. I. Lasiecka Exponential decay rates for the solutions of Euler-Bernoulli equations with boundary dissipation occurring in the moments only J. Differential Equations 95 1992 169 182
14. D. Salamon Infinite-dimensional systems with unbounded control and observation: a functional analytic approach Trans. Amer. Math. Soc. 300 1987 383 431
15. O.J. Staffans Passive and conservative continuous-time impedance and scattering systems. Part I: well-posed systems Math. Control, Signals, Systems 15 2002 291 315
16. M. Tucsnak, and G. Weiss How to get a conservative well-posed linear system out of thin air II, controllability and stability SIAM J. Control Optim. 42 2003 907 935
17. G. Weiss Admissibility of unbounded control operators SIAM J. Control Optim. 27 1989 527 545
18. G. Weiss Admissibility observation operators for linear semigroups Israel J. Math. 65 1989 17 43
19. G. Weiss, The representation of regular linear systems in Hilbert spaces, in: F. Kappel, K. Kunisch, W. Schappacher (Eds.), Control and Estimation of Distributed Parameter Systems, Birkhäuser, Basel, 1989, pp. 401-416.
20. G. Weiss Regular linear systems with feedback Math. Control Signals Systems 7 1994 23 57
21. G. Weiss Transfer functions of regular linear systems I: characterizations of regularity Trans. Amer. Math. Soc. 342 1994 827 854
22. G. Weiss, and R.F. Curtain Dynamic stabilization of regular linear systems IEEE Trans. Auto. Control 42 1997 4 21
23. G. Weiss, and R. Rebarber Optimizability and estimatability for infinite-dimensional linear systems SIAM J. Control Optim. 39 2000 1204 1232
24. G. Weiss, O.J. Staffans, M. Tucsnak, Well-posed linear systems - a survey with emphasis on conservative systems, in: Mathematical Theory of Networks and Systems (Perpignan, 2000), Int. J. Appl. Math. Comput. Sci. 11 (2001) 7-33.
25. G. Weiss, and M. Tucsnak How to get a conservative well-posed linear system out of thin air I, well-posedness and energy balance ESAIM J. Control Optim. Cal. Var. 9 2003 247 274