Infinite dimensional observers for vibrating systems

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2006, Pages 3979-3983

  Xu, Cheng Zhong ^a   Deguenon, Judicaël ^a   Sallet, Gauthier ^b  

^a UNIVERSITÉ LYON 1   (France)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; HILBERT SPACES; KALMAN FILTERS;

ROTATING BEAM SYSTEM; SKEW-ADJOINT GENERATOR; VIBRATING SYSTEMS;

VIBRATION CONTROL;

EID: 39649106291     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2006.377212     Document Type: Conference Paper

References (38)

1. J. BAILLEUL and M. LEVI, Rotational elastic dynamics, Physica 27D, 43-62, 1987.
2. R.F. CURTAIN and A.J. PRITCHARD, Infinite Dimensional Linear Systems, New York, Springer-Verlag, 1978.
3. F. CELLE, J.P. GAUTHIER, D. KAZAKOS and G. SALLET, Synthesis of nonlinear observers: a harmonic analysis approach, Math. System Theory 22, 291-322, 1989.
4. J.P. GAUTHIER, C.Z. XU and A. BOUNABAT, A observer for infinite-dimensional skew-adjoint bilinear systems, Journal of Mathematical Systems Estimation and Control 8, 31-50, 1998.
5. B.Z. GUO, Riesz basis approach to the stabilization of a flexible beam with a tip mass, SIAM J. Control Optim. 39, 1736-1747, 2001.
6. C.Z. XU, Contrôle des Systèmes hybrides, Polycopie du Cours de DEA, Institut de mathématiques et de sciences physiques, Benin, mars 1999.
7. A.E. INGHAM, Some trigonometrical inequalities with applications to the theory of series, Math. Zeischrift 41, 367-379,1936.
8. V. KOMORNIK, Rapid boundary stabilization of linear distributed systems, Prépublication de l'Institut de recherche mathématiques avancée, ISSN 0755-3390, 1-31, 1996.
9. D.L. RUSSELL and G. WEISS, A general necessary conditions for exact observability, SIAM J. Control and Optim. 32, 1-23, 1994.
10. J.P. GAUTHIER and I. KUPKA, A separation principle for bilinear systems with dissipative drifts, IEEE Transaction Automatic Control 25, 1-18, 1991.
11. B.Z. GUO and Z.C SHAO, Regularity of a Schrödinger equation with Dirichlet control and colocated observation, submitted manuscript, 1-11, 2005.
12. B.Z. GUO, K.D. PHUNG and X. ZHANG, The regularity of the wave equation with partial Dirichlet control and colocated observation, submitted manuscript, 1-18, 2005.
13. A. EL JAI, A.J. PRITCHARD, Capteurs et actionneurs dans l'analyse des systèmes distribués, Masson, 1986.
14. G. WEISS, Regular linear systems with feedback, Mathematics of Control, Signals, and Systems 7, 23-57, 1994.
15. A.M. BLOCH and E.S. TITI, On the dynamics of rotating elastic beams, Proc. Conf. New Trends System Theory, Genova, Italy (Conte, Perdon, and Wyman, Eds.), Birkauser, 1990.
16. C.Z. XU and J. BAILLIEUL, Stabilizability and stabilization of a rotating body beam system with torque control, IEEE Transactions Automatic Control 38, 1754-1765, 1993.
17. C.Z. XU and G. SALLET, Boundary stabilization of a rotating flexible system, Lectures Notes in Control and Information Sciences 185 (R.F. Curtain, A. Bensoussan, and J.L. Lions, Eds.), Springer-Verlag, New York, 347-365, 1992.
18. O. MORGUL, Control of a rotating flexible structure, IEEE Transactions Automatic Control 39, 351 - 356, 1994.
19. J.M. CORON and B. D'ANDRÉA-NOVEL, Stabilization of a rotating body-beam without damping, IEEE Transactions Automatic Control 43, 608-618, 1998.
20. B. CHENTOUF and J.F. COUCHOURON, Nonlinear feedback stabilization of a rotating body-beam system, Rapport de recherche de l'INRIA, no.3823, 1999.
21. R.F. CURTAIN and G. WEISS, Exponential stabilization of well-posed systems by colocated feedback, to appear in SIAM J. Contr. Optim., 1-30, 2005.
22. W. KRABS, On Moment Theory and Controllability of One Dimensional Vibrating Systems and Heating Processes, Lecture Notes in Control and Information Sciences 173, Springer-Verlag, Berlin, 1992.
23. V. JURDJEVIC and J.P. QUINN, Controllability and stability, J. Differential Equations 28, 381-389, 1978.
24. H. LAOUSY, C.Z. XU and G. SALLET, Boundary feedback stabilization of a rotating body-beam system, IEEE Transactions Automatic Control 41, 241 - 245, 1996.
25. T.D. NGUYEN and O. EGELAND, Tracking and observer design for a motorized Euler-Bernoulli beam, Proceedings IEEE International Conference on Decision and Control, Maui, Hawaii, 2003.
26. F. CONRAD and M. PIERRE, Stabilization of Euler-Bernouilli beam by nonlinear boundary feedback, Rapport de recherche de l'INRIA, no. 1235, 1990.
27. M.A. DEMETRIOU, Second order observers for second order distributed parameter systems, Systems & Control Letters 51, pp.225-234, 2004.
28. A. PAZY, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York, 1983.
29. E.D. SONTAG, Mathematical Control Theory: Deterministic Finite Dimensional Systems, Springer-Verlag, New York, 1990.
30. M. TUCSNAK and G. WEISS, Simultaneous exact controllability and some applications, SIAM J. Control Optim. 38, 1408-1427, 2000.
31. R. TRIGGIANI, On the stabilizability problem in Banach space, J. Math. Analysis and Applications 52, 383-403, 1975.
32. G. WEISS, Regular linear systems with feedback, Math. Contr., Signals Syst. 7, 23-57, 1994.
33. M. SLEMROD, A note on complete controllability and stabilizability for linear control systems in Hilbert spaces, SIAM J. Contr. Optim. 12, 500-508, 1974.
34. C.Z. XU and G. WEISS, Eigenvalues and eigenvectors of semigroup generators obtained from diagonal generators by feedback, draft, 2002.
35. G. WEISS and R.F. CURTAIN, Exponential stabilization of vibrating systems by collocated feedback, Proc. 7th IEEE Mediterranean Symposium on Control and Automation, Haifa, Israel, June 1999.
36. G. WEISS and R.F. CURTAIN, Exponential stabilization of a Rayleigh beam using colocated control, to appear in IEEE Transactions Automatic Control, 1-24, 2005.
37. C.Z. XU, P. LIGARIUS and J.P. GAUTHIER, An observer for infinite-dimensional dissipative bilinear systems, Computers Math. Apllic. 29, 13-21, 1995.
38. I. LASIECKA, Stabilization of wave and plate-like equations with nonlinear dissipation on the boundary, Journal of Differnrential Equations 79, 340-381, 1989.