Dynamic stabilization of systems via decoupling techniques
Farid Ammar-Khodja; Ahmed Bader; Assia Benabdallah
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 4, page 577-593
- ISSN: 1292-8119
Access Full Article
top
Abstract
topHow to cite
topAmmar-Khodja, Farid, Bader, Ahmed, and Benabdallah, Assia. "Dynamic stabilization of systems via decoupling techniques." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 577-593. <http://eudml.org/doc/197329>.
@article{Ammar2010,
abstract = {
We give sufficient conditions which allow the study of the exponential
stability of systems closely related to the linear thermoelasticity systems
by a decoupling technique. Our approach is based on the multipliers
technique and our result generalizes (from the exponential stability point
of view) the earlier one obtained by Henry et al.},
author = {Ammar-Khodja, Farid, Bader, Ahmed, Benabdallah, Assia},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Stabilization; thermoelasticity.; sufficient conditions; exponential stability; linear thermoelasticity; multiplier technique},
language = {eng},
month = {3},
pages = {577-593},
publisher = {EDP Sciences},
title = {Dynamic stabilization of systems via decoupling techniques},
url = {http://eudml.org/doc/197329},
volume = {4},
year = {2010},
}
TY - JOUR
AU - Ammar-Khodja, Farid
AU - Bader, Ahmed
AU - Benabdallah, Assia
TI - Dynamic stabilization of systems via decoupling techniques
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 577
EP - 593
AB -
We give sufficient conditions which allow the study of the exponential
stability of systems closely related to the linear thermoelasticity systems
by a decoupling technique. Our approach is based on the multipliers
technique and our result generalizes (from the exponential stability point
of view) the earlier one obtained by Henry et al.
LA - eng
KW - Stabilization; thermoelasticity.; sufficient conditions; exponential stability; linear thermoelasticity; multiplier technique
UR - http://eudml.org/doc/197329
ER -
References
top- F. Ammar-Khodja and A. Benabdallah, Sufficient conditions for uniform stabilization of second order equations by dynamic controllers. Dynamics of Continuous, Discrete and Impulsive Systems, to appear.
- F. Ammar-Khodja and A. Benabdallah, Conditions suffisantes pour la stabilisation uniforme d'équations du second ordre par des contrôleurs dynamiques. C.R. Acad. Sci. Sér. I Math.323 (1996) 615-620.
- F. Ammar Khodja, A. Benabdallah and D. Teniou, Coupled systems. Abstract and Appl. Anal.1 (1996) 327-340.
- F.V. Atkinson, H. Langer, R. Mennicken and A.A. Shkalikov, The essential spectrum of some matrix operators. Math. Nachr.167 (1994) 5-20.
- C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary. SIAM J. Control Optim.30 (1992) 1024-1065.
- A.V. Balakrishnan, Applied functional analysis, Springer-Verlag, New-York, Heidelberg (1976).
- Bourgeat A., Simulating gas-liquid flow in a well-reservoir system. Numerical Methods in Engineering and Applied Sciences, H. Adler, J.C. Heinrich, S. Lavanchy, E. Onate and B. Suarez, Eds., CIMNE, Barcelona (1992).
- T. Cazenave and Dickstein F., On the initial value problem for a linear model of well-reservoir coupling (1996) preprint.
- S. Chen and R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems. Pacific J. Math.136 (1989) 15-55.
- R. Dautray and J.L. Lions, Analyse Mathématique et Calcul Numérique2, Masson (1987).
- R.F. Curtain and G. Weiss, Dynamic stabilization of regular linear systems. IEEE Trans. Automat. Contr.42 (1997) 4-21.
- R.F. Curtain and H.J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory. Springer-Verlag, Texts in Applied Mathematics21 (1995).
- K.-J. Engel, Operator matrices and systems of evolution equations (1998).
- A. Haraux, Une remarque sur la stabilisation de certains systemes du deuxième ordre en temps. Portugal Math.46 (1989) 245-258.
- A. Haraux, Systèmes Dynamiques Dissipatifs et Applications, RMA 17, Masson (1991).
- F. Huang, Characteristic conditions for exponential stability of linear dynamic systems in Hilbert spaces. Ann. Diff. Eqs.1 (1985).
- D.B. Henry, O. Lopes and A. Perissinitto Jr., On the essential spectrum of a semigroup of thermoelasticity. Nonlinear Anal., TMA21 (1993) 65-75.
- J.E. Lagnese and J.L. Lions, Modelling Analysis and Control of Thin Plates, RMA 6, Masson (1988).
- Lasiecka I. and Triggiani R., Differential and Algebraic Riccati Equations ..., Springer-Verlag, Lecture Notes in Control and Information Sciences164 (1991).
- Z. Liu and J. Yong, Qualitative properties of certain C0 semigroups arising in elastic systems with various dampings (1998) preprint.
- G. Lebeau and E. Zuazua E., Null controllability of a system of linear thermoelasticity (1995) preprint.
- R. Nagel, Towards a ``Matrix Theory'' for unbounded operators matrices. Math. Z. 201 (1989) 57-68.
- A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, Applied Mathematical Sciences 44 (1983).
- J.E. Munoz Rivera and R. Racke, Smoothing properties, decay and global existence of solutions to nonlinear coupled systems of thermoelastic type. SIAM J. Math. Anal. (1995) 1547-1563.
- D.L. Russell, A comparison of certain elastic dissipation mechanisms via decoupling and projection techniques. Quart. Appl. Math. 49 (1991) 373-396.
- D.L. Russell, A general framework for the study of indirect damping mechanisms in elastic systems, J. Math. Anal. Appl. 173 (1993) 339-358.
- L. De Teresa and E. Zuzua, Controllability for the linear system of thermoelastic plates. Adv. Diff. Eqs. (1996) 369-402.
- J. Zabcyk, Mathematical Control Theory: An Introduction, Birkhauser (1995).
- E. Zuzua, Controllability of the linear system of thermoelasticity. J. Math. Pures Appl.74 (1995) 303-346.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.