Dynamic stabilization of systems via decoupling techniques

Farid Ammar-Khodja; Ahmed Bader; Assia Benabdallah

ESAIM: Control, Optimisation and Calculus of Variations (1999)

  • Volume: 4, page 577-593
  • ISSN: 1292-8119

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Ammar-Khodja, Farid, Bader, Ahmed, and Benabdallah, Assia. "Dynamic stabilization of systems via decoupling techniques." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 577-593. <http://eudml.org/doc/90555>.

@article{Ammar1999,
author = {Ammar-Khodja, Farid, Bader, Ahmed, Benabdallah, Assia},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {sufficient conditions; exponential stability; linear thermoelasticity; multiplier technique},
language = {eng},
pages = {577-593},
publisher = {EDP Sciences},
title = {Dynamic stabilization of systems via decoupling techniques},
url = {http://eudml.org/doc/90555},
volume = {4},
year = {1999},
}

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
PB - EDP Sciences
VL - 4
SP - 577
EP - 593
LA - eng
KW - sufficient conditions; exponential stability; linear thermoelasticity; multiplier technique
UR - http://eudml.org/doc/90555
ER -

References

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  1. [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. Zbl0946.35013MR1411052
  2. [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. Zbl0859.93031MR1411052
  3. [3] F. Ammar Khodja, A. Benabdallah and D. Teniou, Coupled systems. Abstract and Appl. Anal. 1 ( 1996) 327-340. Zbl0936.47024MR1485580
  4. [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. Zbl0831.47001MR1285306
  5. [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. Zbl0786.93009MR1178650
  6. [6] A.V. Balakrishnan, Applied functional analysis, Springer-Verlag, New-York, Heidelberg ( 1976). Zbl0333.93051MR470699
  7. [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. [8] T. Cazenave and Dickstein F., On the initial value problem for a linear model of well-reservoir coupling ( 1996) preprint. Zbl0893.35103MR1411371
  9. [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. Zbl0633.47025MR971932
  10. [10] R. Dautray and J.L. Lions, Analyse Mathématique et Calcul Numérique 2, Masson ( 1987). Zbl0708.35003MR918560
  11. [11] R.F. Curtain and G. Weiss, Dynamic stabilization of regular linear systems. IEEE Trans. Automat. Contr. 42 ( 1997) 4-21. Zbl0876.93074MR1439361
  12. [12] R.F. Curtain and H.J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory. Springer-Verlag, Texts in Applied Mathematics 21 ( 1995). Zbl0839.93001MR1351248
  13. [13] K.-J. Engel, Operator matrices and systems of évolution équations (1998). Zbl0936.34044
  14. [14] A. Haraux, Une remarque sur la stabilisation de certains systèmes du deuxième ordre en temps. Portugal Math. 46 ( 1989) 245-258. Zbl0679.93063MR1021188
  15. [15] A. Haraux, Systèmes Dynamiques Dissipatifs et Applications, RMA 17, Masson ( 1991). Zbl0726.58001MR1084372
  16. [16] F. Huang, Characteristic conditions for exponential stability of linear dynamic systems in Hubert spaces. Ann. Diff. Eqs. 1 ( 1985). Zbl0593.34048MR834231
  17. [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. Zbl0837.73010MR1231529
  18. [18] J.E. Lagnese and J.L. Lions, Modelling Analysis and Control of Thin Plates, RMA6, Masson ( 1988). Zbl0662.73039MR953313
  19. [19] Lasiecka I. and Triggiani R., Differential and Algebraic Riccati Equations..., Springer-Verlag, Lecture Notes in Control and Information Sciences 164 ( 1991). Zbl0754.93038MR1132440
  20. [20] Z. Liu and J. Yong, Qualitative properties of certain C0 semigroups arising in elastic systems with various dampings ( 1998) preprint. Zbl0962.47020MR1665862
  21. [21] G. Lebeau and E. Zuazua E., Null controllability of a system of linear thermoelasticity ( 1995) preprint. Zbl1064.93501MR1620510
  22. [22] R. Nagel, Towards a "Matrix Theory" for unbounded operators matrices. Math. Z. 201 ( 1989) 57-68. Zbl0672.47001MR990188
  23. [23] A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, Applied Mathematical Sciences 44 ( 1983). Zbl0516.47023MR710486
  24. [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. Zbl0842.35039MR1356459
  25. [25] D.L. Russell, A comparison of certain elastic dissipation mechanisms via decoupling and projection techniques. Quart. Appl. Math. 49 ( 1991) 373-396. Zbl0725.73064MR1106398
  26. [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. Zbl0771.73045MR1209323
  27. [27] L. De Teresa and E. Zuzua, Controllability for the linear system of thermoelastic plates. Adv. Diff. Eqs. ( 1996) 369-402. Zbl0853.93017
  28. [28] J. Zabčyk, Mathematical Control Theory: An Introduction, Birkhauser ( 1995). Zbl1071.93500
  29. [29] E. Zuzua, Controllability of the linear system of thermoelasticity. J. Math. Pures Appl. 74 ( 1995) 303-346. Zbl0846.93008MR1341768

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