H. Alwi, C. Edwards, and A. Marcos, Fault reconstruction using a LPV sliding mode observer for a class of LPV systems, Journal of the Franklin Institute, vol.349, issue.2, pp.510-530, 2012.
DOI : 10.1016/j.jfranklin.2011.06.026

M. Blanke, R. Izadi-zamanabadi, S. Bogh, and C. Lunau, Fault-tolerant control systems ??? A holistic view, Control Engineering Practice, vol.5, issue.5, 1997.
DOI : 10.1016/S0967-0661(97)00051-8

M. Blanke, M. Staroswiecki, and N. E. Wu, Concepts and methods in fault-tolerant control, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), pp.2606-2620, 2001.
DOI : 10.1109/ACC.2001.946264

J. Chen and R. J. Patton, Robust model-based fault diagnosis for dynamic systems, 2012.
DOI : 10.1007/978-1-4615-5149-2

L. Chen, R. Patton, and P. Goupil, Application of model-based LPV actuator fault estimation for an industrial benchmark, Control Engineering Practice, vol.56, pp.60-74, 2016.
DOI : 10.1016/j.conengprac.2016.08.003

L. Chen, R. Patton, and P. Goupil, Robust fault estimation using an LPV reference model: ADDSAFE benchmark case study, Control Engineering Practice, vol.49, p.580, 2016.
DOI : 10.1016/j.conengprac.2015.12.006

, Practice, vol.49, pp.194-203

D. Fischer and R. Isermann, Mechatronic semi-active and active vehicle suspensions, Control Engineering Practice, vol.12, issue.11, pp.1353-1367, 2004.
DOI : 10.1016/j.conengprac.2003.08.003

Z. Gao and S. X. Ding, Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems, Automatica, vol.43, issue.5, pp.912-920, 2007.
DOI : 10.1016/j.automatica.2006.11.018

J. Gertler, Fault detection and isolation using parity relations, Control Engineering Practice, vol.5, issue.5, pp.653-661, 1997.
DOI : 10.1016/S0967-0661(97)00047-6

S. Grenaille, D. Henry, and A. Zolghadri, A Method for Designing Fault Diagnosis Filters for LPV Polytopic Systems, Journal of Control Science and Engineering, vol.2008, issue.1, 2008.
DOI : 10.1016/j.conengprac.2005.06.007

URL : https://hal.archives-ouvertes.fr/hal-00181593

L. Guo and L. Zhang, Robust H??? control of active vehicle suspension under non-stationary running, Journal of Sound and Vibration, vol.331, issue.26, pp.5824-5837, 2012.
DOI : 10.1016/j.jsv.2012.07.042

S. Guo, S. Yang, and C. Pan, Dynamic Modeling of Magnetorheological Damper Behaviors, Journal of Intelligent Material Systems and Structures, vol.5, issue.3, pp.620-623, 2006.
DOI : 10.1515/IJNSNS.2005.6.2.139

M. T. Hamayun, C. Edwards, and H. Alwi, Design and analysis of an integral sliding mode fault tolerant control scheme, Fault Tolerant Control Schemes Using Integral Sliding Modes, pp.39-61, 2016.

D. Henry and A. Zolghadri, Design of fault diagnosis filters: A multi-objective approach, Journal of the Franklin Institute, vol.342, issue.4, pp.421-446, 2005.
DOI : 10.1016/j.jfranklin.2005.01.001

URL : https://hal.archives-ouvertes.fr/hal-00164867

D. Hernández-alcántara, J. C. Tudón-martínez, L. Amézquita-brooks, C. A. Vivas-lópez, and R. Morales-menéndez, Modeling, diagnosis and estimation of actuator faults in vehicle suspensions, Control Engineering Practice, vol.49, pp.173-186, 2016.
DOI : 10.1016/j.conengprac.2015.12.002

D. Hrovat, Survey of Advanced Suspension Developments and Related Optimal Control Applications11This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Editor Karl Johan ??str??m.,22Simple, mostly LQ-based optimal control concepts gave useful insight about performance potentials, bandwidth requirements, and optimal structure of advanced vehicle suspensions. The present paper reviews these optimal control applications and related practical developments., Automatica, vol.33, issue.10, pp.1781-1817, 1997.
DOI : 10.1016/S0005-1098(97)00101-5

D. Hrovat and M. Hubbard, A comparison between jerk optimal and acceleration optimal vibration isolation, Journal of Sound and Vibration, vol.112, issue.2, pp.201-210, 1987.
DOI : 10.1016/S0022-460X(87)80189-X

R. Isermann, Supervision, fault-detection and fault-diagnosis methods ??? An introduction, Control Engineering Practice, vol.5, issue.5, pp.639-652, 1997.
DOI : 10.1016/S0967-0661(97)00046-4

, Measurement and Evaluation of mechanical vibration and shock as applied to machines, vehicles and structures. Standard International Organization for Standardization, ISO, vol.8608, p.2016, 2016.

J. Jiang and X. Yu, Fault-tolerant control systems: A comparative study between active and passive approaches, Annual Reviews in Control, vol.36, issue.1, pp.60-72, 2012.
DOI : 10.1016/j.arcontrol.2012.03.005

H. R. Karimi, Observer-based mixed h2/h control design for linear systems with time-varying delays: An lmi approach, International Journal of Control, Automation and Systems, vol.6, pp.1-14, 2008.

M. J. Khosrowjerdi, R. Nikoukhah, and N. Safari-shad, A mixed H2/H??? approach to simultaneous fault detection and control, Automatica, vol.40, issue.2, pp.261-267, 2004.
DOI : 10.1016/j.automatica.2003.09.011

URL : https://hal.archives-ouvertes.fr/inria-00069911

B. Kulcsár and M. Verhaegen, Robust Inversion Based Fault Estimation for Discrete-Time LPV Systems, IEEE Transactions on Automatic Control, vol.57, issue.6, pp.57-1581, 2012.
DOI : 10.1109/TAC.2011.2176160

J. Lofberg, YALMIP : a toolbox for modeling and optimization in MATLAB, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), pp.284-289, 2004.
DOI : 10.1109/CACSD.2004.1393890

F. López-estrada, J. Ponsart, and C. Astorga-zaragoza, Fault estimation observer design for descriptor-LPV systems with unmeasurable gain scheduling functions, 2013 Conference on Control and Fault-Tolerant Systems (SysTol), pp.655-269, 2013.
DOI : 10.1109/SysTol.2013.6693881

M. Mahmoud, J. Jiang, and Y. Zhang, Active fault tolerant control systems: stochastic analysis and synthesis, 2003.

, Mathworks, 2017.

J. Mohammadpour and C. W. Scherer, Control of linear parameter varying systems with applications, 2012.
DOI : 10.1007/978-1-4614-1833-7

M. Moradi and A. Fekih, Adaptive PID-Sliding-Mode Fault-Tolerant Control Approach for Vehicle Suspension Systems Subject to Actuator Faults, IEEE Transactions on Vehicular Technology, vol.63, issue.3, pp.1041-1054, 2014.
DOI : 10.1109/TVT.2013.2282956

M. Q. Nguyen, O. Sename, and L. Dugard, A switched LPV observer for actuator fault estimation, IFAC-PapersOnLine, vol.48, issue.26, pp.194-199, 2015.
DOI : 10.1016/j.ifacol.2015.11.136

URL : https://hal.archives-ouvertes.fr/hal-01226569

M. Q. Nguyen, O. Sename, and L. Dugard, Comparison of observer 670 approaches for actuator fault estimation in semi-active suspension systems, 3rd Conference on Control and Fault-Tolerant Systems, pp.227-232, 2016.

Q. Nguyen and S. Choi, A new approach for dynamic modeling of an electrorheological damper using a lumped parameter method, Smart Materials and Structures, p.115020, 2009.
DOI : 10.1088/0964-1726/18/11/115020

S. De-oca, V. Puig, M. Witczak, and L. Dziekan, Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter, International Journal of Applied Mathematics and Computer Science, vol.32, issue.2, pp.161-171, 2012.
DOI : 10.1016/j.arcontrol.2008.03.008

P. M. Pardalos, A. Migdalas, and L. Pitsoulis, Pareto optimality, game Poussot-Vassal Robust LPV multivariable Automotive Global Chassis Control, C, 2008.

C. Poussot-vassal, O. Sename, L. Dugard, P. Gaspar, Z. Szabo et al., Attitude and handling improvements through gain-scheduled suspensions and brakes control, Control Engineering Practice, vol.19, issue.3, pp.252-263, 2011.
DOI : 10.1016/j.conengprac.2010.05.016

URL : https://hal.archives-ouvertes.fr/hal-00260299

C. Poussot-vassal, C. Spelta, O. Sename, S. M. Savaresi, and L. Dugard, , 2012.

, Survey and performance evaluation on some automotive semi-active suspension control methods: A comparative study on a single-corner model, Annual Reviews in Control, vol.36, pp.148-160

M. Rodrigues, H. Hamdi, D. Theilliol, C. Mechmeche, and N. Braiek, Actuator fault estimation based adaptive polytopic observer for a class of LPV descriptor systems, International Journal of Robust and Nonlinear Control, vol.34, issue.6, pp.673-688, 2015.
DOI : 10.1016/S0005-1098(98)00013-2

D. Rotondo, F. López-estrada, F. Nejjari, J. Ponsart, D. Theilliol et al., Actuator multiplicative fault estimation in discrete-time 700, 2016.

, LPV systems using switched observers, Journal of the Franklin Institute, vol.353, pp.3176-3191

D. Sammier, O. Sename, and L. Dugard, Skyhook and H8 Control of Semi-active Suspensions: Some Practical Aspects, Vehicle System Dynamics, vol.39, issue.4, pp.279-308, 2003.
DOI : 10.1076/vesd.39.4.279.14149

S. M. Savaresi, S. Bittanti, and M. Montiglio, Identification of semiphysical and black-box non-linear models: the case of MR-dampers for vehicles control, Automatica, vol.41, pp.113-127, 2005.

S. M. Savaresi, C. Poussot-vassal, C. Spelta, O. Sename, and L. Dugard, , 2010.

, Semi-active suspension control design for vehicles

C. Scherer, P. Gahinet, and M. Chilali, Multiobjective output-feedback control via LMI optimization, IEEE Transactions on Automatic Control, vol.42, issue.7, pp.896-911, 1997.
DOI : 10.1109/9.599969

O. Sename, J. C. Tudón-martínez, and S. Fergani, LPV methods for fault-tolerant vehicle dynamic control, 2013 Conference on Control and Fault-Tolerant Systems (SysTol), pp.116-130, 2013.
DOI : 10.1109/SysTol.2013.6693821

URL : https://hal.archives-ouvertes.fr/hal-00937237

K. Toh, M. J. Todd, and R. H. Tütüncü, Sdpt3a matlab software package for semidefinite programming, version 1.3. Optimization methods and software, pp.545-581, 1999.

H. E. Tseng and D. Hrovat, State of the art survey: active and semi- 720 active suspension control. Vehicle system dynamics, pp.1034-1062, 2015.

J. C. Tudón-martínez, S. Fergani, O. Sename, J. J. Martinez, R. Morales-menendez et al., Adaptive Road Profile Estimation in Semiactive Car Suspensions, IEEE Transactions on Control Systems Technology, vol.23, issue.6, pp.2293-2305, 2015.
DOI : 10.1109/TCST.2015.2413937

J. C. Tudon-martinez, S. Varrier, O. Sename, R. Morales-menendez, J. Martinez et al., Fault tolerant strategy for semi-active suspensions with LPV accommodation?, 2013 Conference on Control and Fault-Tolerant Systems (SysTol), pp.631-636, 2013.
DOI : 10.1109/SysTol.2013.6693942

URL : https://hal.archives-ouvertes.fr/hal-00937234

J. C. Tudón-martínez, S. Varrier, O. Sename, R. Morales-menendez, J. J. Dugard et al., Fault tolerant strategy for semi-active suspensions with LPV accommodation?, 2013 Conference on Control and Fault-Tolerant Systems (SysTol), pp.631-636, 2013.
DOI : 10.1109/SysTol.2013.6693942

A. Unger, F. Schimmack, B. Lohmann, and R. Schwarz, Application of LQ-based semi-active suspension control in a vehicle, Control Engineering, p.735, 2013.

, Practice, vol.21, pp.1841-1850

C. Vivas-lopez, D. H. Alcántara, M. Q. Nguyen, S. Fergani, G. Buche et al., INOVE: Integrated approach for observation and control of vehicle dynamics, 2010.

C. Vivas-lopez, D. H. Alcántara, M. Q. Nguyen, S. Fergani, G. Buche et al., INOVE: a testbench for the analysis and control of automotive vertical dynamics, 14th International Conference on Vehicle System Dynamics, Identification and Anomalies, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01226502

H. Wang, H. Chen, and Z. Weng, Fault estimation for LPV system with LFT parameter dependence, 2014 IEEE International Conference on Information and Automation (ICIA), pp.560-565, 2014.
DOI : 10.1109/ICInfA.2014.6932717

B. Xiao, Q. Hu, and Y. Zhang, Adaptive Sliding Mode Fault Tolerant Attitude Tracking Control for Flexible Spacecraft Under Actuator Saturation, IEEE Transactions on Control Systems Technology, vol.20, issue.6, pp.1605-1612, 2012.
DOI : 10.1109/TCST.2011.2169796

K. Yamamoto, D. Koenig, O. Sename, and P. Moulaire, Driver torque estimation in electric power steering system using an h ? /h 2 proportional integral observer, Decision and Control (CDC), 2015 IEEE 54th Annual Conference on, pp.843-848, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01235053

K. Zhang, B. Jiang, and W. Chen, An improved adaptive fault estimation design for polytopic LPV systems with application to helicopter models, Asian Control Conference, pp.7-1108, 2009.

K. Zhang, B. Jiang, and V. Cocquempot, Fast adaptive fault estimation and accommodation for nonlinear time-varying delay systems, Asian Journal of Control, vol.52, issue.10, pp.643-652, 2009.
DOI : 10.1111/j.1934-6093.2006.tb00264.x

URL : https://hal.archives-ouvertes.fr/hal-00710935

K. Zhang, B. Jiang, and P. Shi, Observer-based fault estimation and accomodation for dynamic systems, 2012.
DOI : 10.1007/978-3-642-33986-8

Y. Zhang and J. Jiang, Bibliographical review on reconfigurable fault-tolerant control systems, Annual Reviews in Control, vol.32, issue.2, pp.229-252, 2008.
DOI : 10.1016/j.arcontrol.2008.03.008

A. Appendix, Simulation Comparison In this Section, the proposed polytopic LPV FE scheme is compared to a Sliding-Mode fault reconstruction approach This is once again done with a realistic, nonlinear vehicle model. For this, a simple single-step scenario is taken, wherein the loss of effective- 770 ness fault ?(t) decreases at t = 25 s to 0.85. Once again, the same road profile w(t) and PWM signal d c (t) seen in Figure 8 are used. Figure A.16 shows the expected (fault-less) damper force F ER (t) compared to the faulty u f (t) = ?(t)F ER (t), according to the measured outputs y(t), These measured outputs y(t) and the (numerically computed) deflection 775 velocity z def (t) are seen in Figure A.17, 2012.

A. Figure, Simulation Comparison: Faulty and Fault-Free (ideal) ER Damper Force The estimation of??of? of??(t) by both approaches is given in Figure A

, Compared with the very common sliding-mode fault reconstruction approach, 2000.