Dynamic stabilization of systems via decoupling techniques
ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 577-593. 
@article{COCV_1999__4__577_0,
     author = {Ammar-Khodja, Farid and Bader, Ahmed and Benabdallah, Assia},
     title = {Dynamic stabilization of systems via decoupling techniques},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {577--593},
     publisher = {EDP-Sciences},
     volume = {4},
     year = {1999},
     mrnumber = {1746168},
     zbl = {0941.74014},
     language = {en},
     url = {http://archive.numdam.org/item/COCV_1999__4__577_0/}
}
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
PY  - 1999
SP  - 577
EP  - 593
VL  - 4
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/COCV_1999__4__577_0/
LA  - en
ID  - COCV_1999__4__577_0
ER  - 
%0 Journal Article
%A Ammar-Khodja, Farid
%A Bader, Ahmed
%A Benabdallah, Assia
%T Dynamic stabilization of systems via decoupling techniques
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 1999
%P 577-593
%V 4
%I EDP-Sciences
%U http://archive.numdam.org/item/COCV_1999__4__577_0/
%G en
%F COCV_1999__4__577_0
Ammar-Khodja, Farid; Bader, Ahmed; Benabdallah, Assia. Dynamic stabilization of systems via decoupling techniques. ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 577-593. http://archive.numdam.org/item/COCV_1999__4__577_0/

[1] 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. | MR | Zbl

[2] 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. | MR | Zbl

[3] F. Ammar Khodja, A. Benabdallah and D. Teniou, Coupled systems. Abstract and Appl. Anal. 1 ( 1996) 327-340. | MR | Zbl

[4] F.V. Atkinson, H. Langer, R. Mennicken and A.A. Shkalikov, The essential spectrum of some matrix operators. Math. Nachr. 167 ( 1994) 5-20. | MR | Zbl

[5] 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. | MR | Zbl

[6] A.V. Balakrishnan, Applied functional analysis, Springer-Verlag, New-York, Heidelberg ( 1976). | MR | Zbl

[7] 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).

[8] T. Cazenave and Dickstein F., On the initial value problem for a linear model of well-reservoir coupling ( 1996) preprint. | MR

[9] S. Chen and R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems. Pacific J. Math. 136 ( 1989) 15-55. | MR | Zbl

[10] R. Dautray and J.L. Lions, Analyse Mathématique et Calcul Numérique 2, Masson ( 1987). | MR

[11] R.F. Curtain and G. Weiss, Dynamic stabilization of regular linear systems. IEEE Trans. Automat. Contr. 42 ( 1997) 4-21. | MR | Zbl

[12] R.F. Curtain and H.J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory. Springer-Verlag, Texts in Applied Mathematics 21 ( 1995). | MR | Zbl

[13] K.-J. Engel, Operator matrices and systems of évolution équations ( 1998). | Zbl

[14] A. Haraux, Une remarque sur la stabilisation de certains systèmes du deuxième ordre en temps. Portugal Math. 46 ( 1989) 245-258. | MR | Zbl

[15] A. Haraux, Systèmes Dynamiques Dissipatifs et Applications, RMA 17, Masson ( 1991). | MR | Zbl

[16] F. Huang, Characteristic conditions for exponential stability of linear dynamic systems in Hubert spaces. Ann. Diff. Eqs. 1 ( 1985). | MR | Zbl

[17] D.B. Henry, O. Lopes and A. Jr. Perissinitto, On the essential spectrum of a semigroup of thermoelasticity. Nonlinear Anal., TMA 21 ( 1993) 65-75. | MR | Zbl

[18] J.E. Lagnese and J.L. Lions, Modelling Analysis and Control of Thin Plates, RMA6, Masson ( 1988). | MR | Zbl

[19] Lasiecka I. and Triggiani R., Differential and Algebraic Riccati Equations..., Springer-Verlag, Lecture Notes in Control and Information Sciences 164 ( 1991). | MR | Zbl

[20] Z. Liu and J. Yong, Qualitative properties of certain C0 semigroups arising in elastic systems with various dampings ( 1998) preprint. | MR | Zbl

[21] G. Lebeau and E. Zuazua E., Null controllability of a system of linear thermoelasticity ( 1995) preprint. | MR | Zbl

[22] R. Nagel, Towards a "Matrix Theory" for unbounded operators matrices. Math. Z. 201 ( 1989) 57-68. | MR | Zbl

[23] A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, Applied Mathematical Sciences 44 ( 1983). | MR | Zbl

[24] 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. | MR | Zbl

[25] D.L. Russell, A comparison of certain elastic dissipation mechanisms via decoupling and projection techniques. Quart. Appl. Math. 49 ( 1991) 373-396. | MR | Zbl

[26] D.L. Russell, A general framework for the study of indirect damping mechanisms in elastic systems. J. Math. Anal. Appl. 173 ( 1993) 339-358. | MR | Zbl

[27] L. De Teresa and E. Zuzua, Controllability for the linear system of thermoelastic plates. Adv. Diff. Eqs. ( 1996) 369-402. | Zbl

[28] J. Zabčyk, Mathematical Control Theory: An Introduction, Birkhauser ( 1995). | Zbl

[29] E. Zuzua, Controllability of the linear system of thermoelasticity. J. Math. Pures Appl. 74 ( 1995) 303-346. | MR | Zbl