I. D. Aiken, D. K. Nims, A. S. Whittaker, and J. M. Kelly, Overview of the application of active/semi active control to building structures in japan, Earthquake Spectra, vol.9, 1993.

G. Allaire, Analyse Numérique et Optimisation. Edition Ellipses, 2005.

A. Astolfi, D. Karagiannis, and R. Ortega, Towards applied nonlinear adaptive control, Annual Reviews in Control, vol.32, issue.2, pp.136-148, 2008.
DOI : 10.1016/j.arcontrol.2008.08.003

M. J. Balas, Active control of flexible systems, Journal of Optimization Theory and Applications, vol.18, issue.3, pp.415-436, 1978.
DOI : 10.1007/BF00932903

P. Banerji, M. Murudi, A. H. Shah, and N. Popplewell, Tuned liquid dampers for controlling earthquake response of structures, Earthquake Engineering & Structural Dynamics, vol.25, issue.44, pp.587-602, 2000.
DOI : 10.1002/(SICI)1096-9845(200005)29:5<587::AID-EQE926>3.0.CO;2-I

L. Bardella and F. Genna, Newmark???s Time Integration Method From the Discretization of Extended Functionals, Journal of Applied Mechanics, vol.72, issue.4, pp.527-537, 2005.
DOI : 10.1115/1.1934648

R. C. Barros, Seismic response of tanks and vibration control of their pipelines, Journal of Vibroengineering, vol.4, issue.1, pp.9-16, 2002.

C. Scott and . Beeler, State dependent roccati equation regulation of systems with state and control nonlinearities, NASA and National Institute of Aerospace, 2004.

P. Bisegna, G. Caruso, and F. Maceri, Optimized electric networks for vibration damping of piezoactuated beams, Journal of Sound and Vibration, vol.289, issue.4-5, pp.117-122, 2006.
DOI : 10.1016/j.jsv.2005.02.045

F. Bourquin, B. Branchet, and M. Collet, Hybridation primale-duale pour la mise en oeuvre du contrôle actif de structure, actes du 7ème colloque national en calcul de structures, 2005.

F. Bourquin, J. S. Briffaut, and M. Collet, On the feedback stabilisation: Komornik method, Second international symposium on active control in mechanical engineering, 1997.

F. Bourquin, M. Collet, and L. Ratier, MODELING AND NUMERICAL ISSUES IN THE ACTIVE CONTROL OF FLEXIBLE STRUCTURES, Structural Control for Civil and Infrastructure Engineering, 2000.
DOI : 10.1142/9789812811707_0011

H. Cao and Q. S. Li, New control strategies for active tuned mass damper systems, Computers & Structures, vol.82, issue.27, pp.2341-2350, 2004.
DOI : 10.1016/j.compstruc.2004.05.010

B. Clement, G. D. , and S. Mauffrey, Aerospace launch vehicle control: a gain scheduling approach, Control Engineering Practice, vol.13, issue.3, pp.333-347, 2005.
DOI : 10.1016/j.conengprac.2003.12.013

R. Collin, B. Basu, and B. M. Broderick, Bang-Bang and Semiactive Control with Variable Stiffness TMDs, Journal of Structural Engineering, vol.134, issue.2, pp.310-317, 2008.
DOI : 10.1061/(ASCE)0733-9445(2008)134:2(310)

M. C. Constantinou, P. Tsopelas, W. Hammel, and A. N. Sigaher, Toggle-Brace-Damper Seismic Energy Dissipation Systems, Journal of Structural Engineering, vol.127, issue.2, pp.105-112, 2001.
DOI : 10.1061/(ASCE)0733-9445(2001)127:2(105)

O. Corbi, Shape memory alloys and their application in structural oscillations attenuation, Simulation Modelling Practice and Theory, vol.11, issue.5-6, pp.387-402, 2003.
DOI : 10.1016/S1569-190X(03)00057-1

O. Corbi, Active and Semi-active Control in civil Engineering, 2007.

M. Couillard, P. Micheau, and P. Masson, Improved clipped periodic optimal control for semi-active harmonic disturbance rejection, Journal of Sound and Vibration, vol.318, issue.4-5, pp.737-756, 2008.
DOI : 10.1016/j.jsv.2008.04.034

O. Coulaud, Un nouveau sch??ma symplectique pour le couplage entre une m??thode du continuum et la dynamique mol??culaire, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.333, issue.3, pp.255-260, 2001.
DOI : 10.1016/S0764-4442(01)02024-9

D. J. Leith, A. Tsourdos, B. A. White, and W. E. Leitead, Application of velocity-based gain-scheduling to lateral auto-pilot design for an agile missile, Control Engineering Practice, vol.9, issue.10, pp.1079-1093, 2001.
DOI : 10.1016/S0967-0661(01)00077-6

D. J. Leith, W. E. Leitead-]-d, W. E. Leith, and . Leitead, Gain-scheduled and nonlinear systems: Dynamic analysis by velocity-based linearization families, International Journal of Control, vol.70, issue.2, pp.289-317, 1998.
DOI : 10.1080/002071798222415

D. J. Leith and W. E. Leitead, Survey of gain-scheduling analysis and design, International Journal of Control, vol.73, issue.11, pp.1001-1025, 2000.
DOI : 10.1080/002071700411304

B. Egarodt, Stability and Adaptive Controllers, 1979.
DOI : 10.1007/BFb0005037

E. Evrin-bilge, Analysis and Real Time Implementation of State- Dependent Riccati Equations Controlled Systems, 2001.

L. C. Evans, An introdution to mathematical optimal control theory version 0.2

K. C. Falcon, B. J. Stine, W. D. Simcock, and C. Andrew, Optimization of vibration absorbers: a graphical method for use on idealized systems with restricted damping, ARCHIVE: Journal of Mechanical Engineering Science 1959-1982 (vols 1-23), vol.9, issue.5, pp.374-381, 1967.
DOI : 10.1243/JMES_JOUR_1967_009_058_02

P. De-fonseca, P. Sas, and H. Van-brussel, ROBUST DESIGN AND ROBUST STABILITY ANALYSIS OF ACTIVE NOISE CONTROL SYSTEMS, Journal of Sound and Vibration, vol.243, issue.1, pp.23-42, 2001.
DOI : 10.1006/jsvi.2000.3406

R. R. Gerges and B. J. Vickery, Wind tunnel study of the across-wind response of a slender tower with a nonlinear tuned mass damper, Journal of Wind Engineering and Industrial Aerodynamics, vol.91, issue.8, pp.1069-1092, 2003.
DOI : 10.1016/S0167-6105(03)00053-9

J. Pieter and D. Hartog, Mechanical Vibrations, Third Edition, 1947.

P. Hauret and P. L. Tallec, Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.37-40, pp.4890-4916, 2006.
DOI : 10.1016/j.cma.2005.11.005
URL : https://hal.archives-ouvertes.fr/hal-00111458

M. Hayati and B. Karami, Design of fully differential cmos amplifier for clipping control circuit, World Applied Sciences Journal, vol.3, issue.1, pp.110-113, 2008.

J. K. Hedrick and A. Girard, Control of nonlinear dynamic systems: Theory and applications

R. Heuer and S. M. Yousefi, On the nonlinear influence of tunes pendulum dampers in slender structures, Fourth European Conference on the Structural Control, 2008.

C. Hirunyapruk, Vibration Control Using an adaptive Tuned Magneto-Rheological Fluid Vibration Absorber, Science and Mathematics, 2009.

J. R. Thomas and . Hughes, Finite Element Method, Linear Static and Dynamic Finite Element Analysis, 1987.

A. Petros, P. V. Ioannou, and . Kokotovic, Adaptive Systems with Reduced Models, 1983.

I. Ioi and K. Ikeda, On the Dynamic Vibration Damped Absorber of the Vibration System, Bulletin of JSME, vol.21, issue.151, pp.21-15164, 1978.
DOI : 10.1299/jsme1958.21.64

A. Isidori, Nonlinear Control System: An Introduction, 1985.
DOI : 10.1007/BFb0006368

C. Kane, J. E. Marsdenad, M. Ortiz, and M. West, Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems, International Journal for Numerical Methods in Engineering, vol.76, issue.10, 1999.
DOI : 10.1002/1097-0207(20001210)49:10<1295::AID-NME993>3.0.CO;2-W

R. Kanitkar, M. Harms, P. Crosby, and M. L. Lai, Seismic retrofit of steel moment frame structure using viscoelastic dampers, ISET Journal of Earthquake Technology, vol.35, pp.207-219, 1998.

K. Hassan and . Khalil, Nonlinear systems, second edition, 1996.

L. Kharevych, Y. Weiwei, E. Tong, J. E. Kanso, P. Marsden et al., Geometric, variational integrators for computer animation, Eurographics/ACM SIGGRAPH Symposium on Computer Animation, 2006.

W. S. Koon and J. E. Marsden, The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems, 48] H. Kwakernaak. Linear Optimal Control Systems. Wiley and Sons NY, pp.21-62, 1972.
DOI : 10.1016/S0034-4877(97)85617-0

S. Lall and M. West, Discrete variational Hamiltonian mechanics, Journal of Physics A: Mathematical and General, vol.39, issue.19, pp.5509-5519, 2006.
DOI : 10.1088/0305-4470/39/19/S11

E. Leboucher, P. Micheau, A. Berry, and A. L. Espérance, A stability analysis of a decentralized adaptive feedback active control system of sinusoidal sound in free space, The Journal of the Acoustical Society of America, vol.111, issue.1, pp.189-199, 2002.
DOI : 10.1121/1.1427358

M. Leon, D. Martin, D. Diego, and A. Santamaria-merino, Discrete variational integrators and optimal control theory, Advances in Computational Mathematics, vol.266, issue.2/3, pp.251-268, 2007.
DOI : 10.1007/s10444-004-4093-5

A. Lew, J. E. Marsden, M. Ortiz, and M. West, Variational time integrators, International Journal for Numerical Methods in Engineering, vol.60, issue.1, pp.153-212, 2004.
DOI : 10.1002/nme.958

S. Leyendecker, S. Ober-blöbaum, J. E. Marsden, and M. Ortiz, Discrete mechanics and optima control for constrained multibody dynamics, International Design Engneering Technical Conferencs & Computers and Information in Engineering Conference, 2007.

Z. Li, J. Tang, and Q. S. Li, Optimal sensor locations for structural vibration measurements, Applied Acoustics, vol.65, issue.8, pp.807-818, 2004.
DOI : 10.1016/j.apacoust.2003.12.007

R. W. Luft, Optimal tuned mass dampers for buildings, Journal of the Structural Division ASCE, vol.105, pp.2766-2772, 1979.

J. E. Marsden and M. West, Discrete mechanics and variational integrators, Acta Numerica 2001, vol.10, pp.357-514, 2001.
DOI : 10.1017/S096249290100006X
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.9551

L. Meirovitch, Dynamics and Control of Disturbed Structures, 1988.

L. Meirovitch, Dynamics and Control of Structures, 1990.

O. B. Mekki, F. Bourquin, M. Debbabi, F. Maceri, and C. Nguyen-van-phu, Some applications of passive and semi-active control devices for harmonic vibrations damping in cable-stayed bridges, Associazione Italiana per l'Analisi delle Sollecitazioni, XXXVII Convegno Nazionale, 2008.

O. B. Mekki, F. Bourquin, F. Maceri, and C. Nggyen-van-phu, An adaptive pendulum for evolving structures. Structural Control and Health Monitoring, pp.1-6, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01055373

M. Othman-ben, Amortissement Semi-Actif des structures flexibles Dipartimento d'ingegneria Civile dell, 2006.

F. Othman-ben-mekki, F. Maceri, and . Bourquin, Amortissement semiactif des structures flexibles: Application au contrôle des grands ponts, XXVème Rencontre Universitaire de Génie Civil, 2007.

S. Müller and M. Ortiz, On the ??-convergence of discrete dynamics and variational integrators, Journal of Nonlinear Science, vol.106, issue.3, pp.279-296, 2004.
DOI : 10.1007/BF02666023

S. Kumpati, A. M. Narendra, and . Annaswamy, Stability of Adaptive Controllers, 2005.

M. Neubauer and J. Wallaschek, Piezoelectrical and experimantal investitation of the frequency ration and switching law for piezoeletic switching techniques, Smart Materials and structures, p.35003, 2008.

M. Nathan, F. Newmark, and . Asce, A method of computation for structural dynamics Journal of the engineering machanics division, 1959.

A. Nishitani and Y. Inoue, Overview of the application of active/semi active control to building structures in japan. Earthquake Engineering and structural dynamics, pp.1565-1574, 2001.

K. Ohno, M. Shimoda, and T. Savada, Optimal design of a tuned liquid damper using a magnetic fluid with one electromagnet, Journal of Physics: Condensed Matter, vol.20, issue.20, p.204146, 2008.
DOI : 10.1088/0953-8984/20/20/204146

R. Palm and U. Rehfuess, Fuzzy controllers as gain scheduling approximators. Fuzzy Sets and systems, pp.233-246, 1997.

P. Curtis, J. R. Mracek, and . Cloutier, Control design for nonlinear benchmark problem via the state-dependent riccati equation method, International Journal of Robust and Nonlinear Control, vol.8, pp.401-433, 1998.

V. Prakash and A. D. Pandey, Vibration isolation using active control systems for civil engineering structures, Bulletin of the Indian Society of Earthquake Technology, vol.26, pp.25-38, 1989.

E. Prempain and I. Postlethwaite, <mml:math altimg="si2.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi mathvariant="script">L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>??and <mml:math altimg="si3.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>??performance analysis and gain-scheduling synthesis for parameter-dependent systems, Automatica, vol.44, issue.8, pp.2081-2089, 2008.
DOI : 10.1016/j.automatica.2007.12.008

]. A. Preumont, Vibration control of active structures, An introduction, 1997.

R. Rana and T. T. Soong, Parametric study and simplified design of tuned mass dampers, Engineering Structures, vol.20, issue.3, pp.193-204, 1998.
DOI : 10.1016/S0141-0296(97)00078-3

F. Ravigan, G. Manolea, and N. Boteanu, The design of a magnetorheological controller, pp.1842-4805, 2008.

F. Ricciardelli, A. Occhiuzzi, and P. Clemente, Semi-active Tuned Mass Damper control strategy for wind-excited structures, Journal of Wind Engineering and Industrial Aerodynamics, vol.88, issue.1, pp.57-74, 2000.
DOI : 10.1016/S0167-6105(00)00024-6

F. Rüdinger, Tuned mass damper with fractional derivative damping, Engineering Structures, vol.28, issue.13, pp.1774-1779, 2006.
DOI : 10.1016/j.engstruct.2006.01.006

I. Sadek, I. Kucuk, E. Zeini, and S. Adali, Optimal boundary control of dynamics responses of piezo actuating micro-beams, Applied Mathematical Modelling, vol.33, issue.8, pp.3343-3353, 2009.
DOI : 10.1016/j.apm.2008.11.009

J. T. Scruggs, Structural Control Using Regenerative Force Actuation Networks, 2004.

J. T. Scruggs and W. D. Iwan, Control of a Civil Structure Using an Electric Machine with Semiactive Capability, Journal of Structural Engineering, vol.129, issue.7, pp.951-959, 2003.
DOI : 10.1061/(ASCE)0733-9445(2003)129:7(951)

M. Setareh, Floor vibration control using semi-active tuned mass dampers, Canadian Journal of Civil Engineering, vol.29, issue.1, pp.76-84, 2002.
DOI : 10.1139/l01-063

A. Shamma, Analysis of gain scheduled control for nonlinear plants, IEEE Transactions on Automatic Control, vol.35, issue.8, pp.898-907, 1990.
DOI : 10.1109/9.58498

J. S. Shamma, Analysis and Design of Gain Scheduled Control Systems, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 1988.

H. Shulte and H. Hahn, Fuzzy state feedback gain scheduling control of servo-pneumatic actuators, Control Engineering Practice, vol.12, issue.5, pp.639-650, 2004.
DOI : 10.1016/S0967-0661(03)00148-5

N. M. Singh, J. Dubey, and G. Laddha, Control of pendulum on a cart with state dependent riccati equations, Proceedings of World Acadamy of Science, Engineering and Technology, vol.3, 2008.

G. Soog, N. Ma, and H. Li, Applications of shape memory alloys in civil structures, Engineering Structures, vol.28, pp.1266-1274, 2006.

T. T. Soong and G. F. Darghouch, Passive Energy dissipation systems in structural engineering, 1997.

M. D. Symans and M. C. Constantinou, SEISMIC TESTING OF A BUILDING STRUCTURE WITH A SEMI-ACTIVE FLUID DAMPER CONTROL SYSTEM, Earthquake Engineering & Structural Dynamics, vol.26, issue.7, pp.759-777, 1997.
DOI : 10.1002/(SICI)1096-9845(199707)26:7<759::AID-EQE675>3.0.CO;2-E

W. T. Thompson, Theory of Vibration with applications, Second Edition, 1981.

G. B. Warburton, Optimum absorber parameters for various combinations of response and excitation parameters, Earthquake Engineering & Structural Dynamics, vol.77, issue.3, pp.327-343, 1988.
DOI : 10.1002/eqe.4290100304

J. K. Yu, T. Wakahara, and D. Reed, A non-linear numerical model of the tuned liquid damper. Earthquake Engineering and structural dynamics, pp.671-686, 1999.