Robust control design for vehicle active suspension systems with uncertainty

A vehicle active suspension system, in comparison with its counterparts, plays a crucial role in adequately guarantee the stability of the vehicle and improve the suspension performances. With a full understanding of the state of the art in vehicle control systems, this thesis identifies key issues in robust control design for active suspension systems with uncertainty, contributes to enhance the suspension performances via handling tradeoffs between ride comfort, road holding and suspension deflection. Priority of this thesis is to emphasize the contributions in handing actuator-related challenges and suspension model parameter uncertainty. The challenges in suspension actuators are identified as time-varying actuator delay and actuator faults. Time-varying delay and its effects in suspension actuators are targeted and analyzed. By removing the assumptions from the state of the art methods, state-feedback and output-feedback controller design methods are proposed to design less conservative state-feedback and output-feedback controller existence conditions. It overcomes the challenges brought by generalized timevarying actuator delay. On the other hand, a novel fault-tolerant controller design algorithm is developed for active suspension systems with uncertainty of actuator faults. A continuous-time homogeneous Markov process is presented for modeling the actuator failure process. The fault-tolerant H∞ controller is designed to guarantee asymptotic the stability, H∞ performance, and the constrained performance with existing possible actuator failures. It is evident that vehicle model parameter uncertainty is a vital factor affecting the performances of suspension control system. Consequently, this thesis presents two robust control solutions to overcome suspension control challenges with nonlinear constraints. A novel fuzzy control design algorithm is presented for active suspension systems with uncertainty. By using the sector nonlinearity method, Takagi-Sugeno (T-S) fuzzy systems are used to model the system. Based on Lyapunov stability theory, a new reliable fuzzy controller is designed to improve suspension performances. A novel adaptive sliding mode controller design approach is also developed for nonlinear uncertain vehicle active suspension systems. An adaptive sliding mode controller is designed to guarantee the stability and improve the suspension performances. In conclusion, novel control design algorithms are proposed for active suspension systems with uncertainty in order to guarantee and improve the suspension performance. Simulation results and comparison with the state of the art methods are provided to evaluate the effectiveness of the research contributions. The thesis shows insights into practical solutions to vehicle active suspension systems, it is expected that these algorithms will have significant potential in industrial applications and electric vehicles industry.

[1]  Hong Chen,et al.  Constrained Control of Active Suspensions: An LMI Approach , 2005 .

[2]  David Crolla,et al.  ACTIVE SUSPENSION CONTROL; PERFORMANCE COMPARISONS USING CONTROL LAWS APPLIED TO A FULL VEHICLE MODEL , 1991 .

[3]  Toshio Yoshimura,et al.  CONSTRUCTION OF AN ACTIVE SUSPENSION SYSTEM OF A QUARTER CAR MODEL USING THE CONCEPT OF SLIDING MODE CONTROL , 2001 .

[4]  Peng Shi,et al.  Fault Detection for Uncertain Fuzzy Systems: An LMI Approach , 2007, IEEE Transactions on Fuzzy Systems.

[5]  Huai-Ning Wu,et al.  Reliable LQ fuzzy control for continuous-time nonlinear systems with actuator faults , 2004, IEEE Trans. Syst. Man Cybern. Part B.

[6]  Shengyuan Xu,et al.  Delay-dependent H ∞ controller design for linear neutral systems with discrete and distributed delays , 2007, Int. J. Syst. Sci..

[7]  Honghai Liu,et al.  An Interval Fuzzy Controller for Vehicle Active Suspension Systems , 2010, IEEE Transactions on Intelligent Transportation Systems.

[8]  Honghai Liu,et al.  Adaptive fuzzy logic controller for vehicle active suspensions with interval type-2 fuzzy membership functions , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[9]  C. Scherer An efficient solution to multi-objective control problems with LMI objectives , 2000 .

[10]  Xingyu Wang,et al.  Sliding mode control for Itô stochastic systems with Markovian switching , 2007, Autom..

[11]  Haiping Du,et al.  Constrained H∞ control of active suspension for a half-car model with a time delay in control , 2008 .

[12]  Yurong Liu,et al.  A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances , 2010, Autom..

[13]  Haiping Du,et al.  Fuzzy Control for Nonlinear Uncertain Electrohydraulic Active Suspensions With Input Constraint , 2009, IEEE Trans. Fuzzy Syst..

[14]  Huijun Gao,et al.  ℋ ∞ model reduction for linear parameter-varying systems with distributed delay , 2009, Int. J. Control.

[15]  Donghua Zhou,et al.  RELIABLE MEMORY FEEDBACK DESIGN FOR A CLASS OF NONLINEAR FUZZY SYSTEMS WITH TIME-VARYING DELAY , 2006 .

[16]  Honghai Liu,et al.  Fault-tolerant H∞ control for active suspension vehicle systems with actuator faults , 2012, J. Syst. Control. Eng..

[17]  Wei-Hsin Liao,et al.  Vibration control of a suspension system via a magnetorheological fluid damper , 2000, Symposium on Applied Photonics.

[18]  Gang Feng,et al.  Reliable H∞ control for discrete-time piecewise linear systems with infinite distributed delays , 2009, at - Automatisierungstechnik.

[19]  Gary J. Balas,et al.  Road adaptive active suspension design using linear parameter-varying gain-scheduling , 2002, IEEE Trans. Control. Syst. Technol..

[20]  Tzuu-Hseng S. Li,et al.  GA-based fuzzy PI/PD controller for automotive active suspension system , 1999, IEEE Trans. Ind. Electron..

[21]  Tong Heng Lee,et al.  LMI Approach to Analysis and Control of Takagi-Sugeno Fuzzy Systems with Time Delay (Lecture Notes in Control and Information Sciences) , 2007 .

[22]  Elbrous M. Jafarov,et al.  Robust sliding-mode control for the uncertain MIMO aircraft model F-18 , 2000, IEEE Trans. Aerosp. Electron. Syst..

[23]  Masao Nagai Recent Researches on Active Suspensions for Ground Vehicles , 1993 .

[24]  Honghai Liu,et al.  Actuator delayed active vehicle suspension control: A T-S fuzzy approach , 2011, 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011).

[25]  Jung-Shan Lin,et al.  Nonlinear design of active suspensions , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[26]  Masashi Yamashita,et al.  H, CONTROL OF AN AUTOMOTIVE ACTIVE SUSPENSION , 1990 .

[27]  Jun Wang,et al.  Mixed GL2/H2/GH2 control with pole placement and its application to vehicle suspension systems , 2001 .

[28]  M. F. Golnaraghi,et al.  Semi-active Vibration Control Schemes for Suspension Systems Using Magnetorheological Dampers , 2006 .

[29]  An-Chyau Huang,et al.  Adaptive sliding control of active suspension systems with uncertain hydraulic actuator dynamics , 2003 .

[30]  Charles Poussot-Vassal,et al.  A methodology for optimal semi-active suspension systems performance evaluation , 2010, 49th IEEE Conference on Decision and Control (CDC).

[31]  Yong-Yan Cao,et al.  Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach , 2000, IEEE Trans. Fuzzy Syst..

[32]  James Lam,et al.  Parameter-dependent input-delayed control of uncertain vehicle suspensions , 2008 .

[33]  Ebrahim Esmailzadeh,et al.  Optimal Active Vehicle Suspensions with Full State Feedback Control , 1992 .

[34]  Yugang Niu,et al.  Robust Fuzzy Design for Nonlinear Uncertain Stochastic Systems via Sliding-Mode Control , 2007, IEEE Transactions on Fuzzy Systems.

[35]  Kisaburo Hayakawa,et al.  Robust H∞-output feedback control of decoupled automobile active suspension systems , 1999, IEEE Trans. Autom. Control..

[36]  Shiuh-Jer Huang,et al.  A new model-free adaptive sliding controller for active suspension system , 2008, Int. J. Syst. Sci..

[37]  Honghai Liu,et al.  Multi-objective H ∞ control for vehicle active suspension systems with random actuator delay , 2012, Int. J. Syst. Sci..

[38]  Daniel W. C. Ho,et al.  Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation , 2010, Autom..

[39]  Bing Chen,et al.  A Delay-Dependent Approach to Robust H∞ Control for Uncertain Stochastic Systems with State and Input Delays , 2009, Circuits Syst. Signal Process..

[40]  Weichao Sun,et al.  Vibration control for active seat suspension systems via dynamic output feedback with limited frequency characteristic , 2011 .

[41]  Chiou-Jye Huang,et al.  NONLINEAR BACKSTEPPING CONTROL DESIGN OF HALF-CAR ACTIVE SUSPENSION SYSTEMS. , 2003 .

[42]  Seung-Bok Choi,et al.  Field test results of a semi-active ER suspension system associated with skyhook controller , 2001 .

[43]  Hong Chen,et al.  A multi-objective control design for active suspensions with hard constraints , 2003, Proceedings of the 2003 American Control Conference, 2003..

[44]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[45]  Hong Chen,et al.  Multiobjective output-feedback suspension control on a half-car model , 2003, Proceedings of 2003 IEEE Conference on Control Applications, 2003. CCA 2003..

[46]  Hong Chen,et al.  Disturbance attenuation control of active suspension with non-linear actuator dynamics , 2011 .

[47]  Hong Chen,et al.  An LMI approach to multiobjective RMS gain control for active suspensions , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[48]  Charles Poussot-Vassal,et al.  A new semi-active suspension control strategy through LPV technique , 2008 .

[49]  James Lam,et al.  Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities , 2008, IEEE Transactions on Automatic Control.

[50]  Jan A. Snyman,et al.  Optimisation of road vehicle passive suspension systems. Part 2. Qualification and case study , 2003 .

[51]  G. Feng,et al.  A Survey on Analysis and Design of Model-Based Fuzzy Control Systems , 2006, IEEE Transactions on Fuzzy Systems.

[52]  Yuanqing Xia,et al.  Robust Adaptive Sliding-Mode Control for Fuzzy Systems With Mismatched Uncertainties , 2010, IEEE Transactions on Fuzzy Systems.

[53]  Chong Lin,et al.  Delay‐dependent robust stability for stochastic time‐delay systems with polytopic uncertainties , 2008 .

[54]  Honghai Liu,et al.  Parameter-dependent robust stability for uncertain Markovian jump systems with time delay , 2011, J. Frankl. Inst..

[55]  Zidong Wang,et al.  Robust Fault-Tolerant Control for a Class of Nonlinear Stochastic Systems With Variance Constraints , 2010 .

[56]  Tsu-Tian Lee,et al.  Neural-network-based optimal fuzzy control design for half-car active suspension systems , 2005, IEEE Proceedings. Intelligent Vehicles Symposium, 2005..

[57]  Jianliang Wang,et al.  Reliable robust flight tracking control: an LMI approach , 2002, IEEE Trans. Control. Syst. Technol..

[58]  Guo-Ping Liu,et al.  Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2004, Syst. Control. Lett..

[59]  Dae Sung Joo,et al.  Sliding mode neural network inference fuzzy logic control for active suspension systems , 2002, IEEE Trans. Fuzzy Syst..

[60]  Ruey-Jing Lian,et al.  Self-organizing fuzzy control of active suspension systems , 2005, Int. J. Syst. Sci..

[61]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[62]  Honghai Liu,et al.  A study on half-vehicle active suspension control using sampled-data control , 2011, 2011 Chinese Control and Decision Conference (CCDC).

[63]  Huijun Gao,et al.  Robust control synthesis for seat suspension systems with actuator saturation and time-varying input delay , 2010 .

[64]  D. Hrovat,et al.  Survey of Advanced Suspension Developments and Related Optimal Control Applications, , 1997, Autom..

[65]  Daniel W. C. Ho,et al.  A note on the robust stability of uncertain stochastic fuzzy systems with time-delays , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[66]  Huijun Gao,et al.  New delay-range-dependent stability condition for linear system , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[67]  M. V. C. Rao,et al.  A tunable fuzzy logic controller for vehicle-active suspension systems , 1997, Fuzzy Sets Syst..

[68]  Wang Changhong,et al.  Sliding mode H∞ control for a class of uncertain nonlinear state-delayed systems , 2006 .

[69]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[70]  Zidong Wang,et al.  H∞ Reliable Control of Uncertain Linear State Delayed Systems , 2004 .

[71]  Hak-Keung Lam,et al.  Quadratic-Stability Analysis of Fuzzy-Model-Based Control Systems Using Staircase Membership Functions , 2010, IEEE Transactions on Fuzzy Systems.

[72]  Daniel W. C. Ho,et al.  Robust $H_{\infty }$ Fuzzy Output-Feedback Control With Multiple Probabilistic Delays and Multiple Missing Measurements , 2010, IEEE Transactions on Fuzzy Systems.

[73]  Honghai Liu,et al.  Reliable Fuzzy Control for Active Suspension Systems With Actuator Delay and Fault , 2012, IEEE Transactions on Fuzzy Systems.

[74]  Aleksander Hac,et al.  Optimal linear preview control of active vehicle suspension , 1990, 29th IEEE Conference on Decision and Control.

[75]  Nong Zhang,et al.  H∞ control of active vehicle suspensions with actuator time delay , 2007 .

[76]  Peng Shi,et al.  H∞ fuzzy output feedback control design for nonlinear systems: an LMI approach , 2003, IEEE Trans. Fuzzy Syst..

[77]  Marios M. Polycarpou,et al.  Adaptive fault-tolerant control of nonlinear uncertain systems: an information-based diagnostic approach , 2004, IEEE Transactions on Automatic Control.

[78]  Guang-Hong Yang,et al.  Adaptive logic‐based switching fault‐tolerant controller design for nonlinear uncertain systems , 2011 .

[79]  Heinz Unbehauen,et al.  Robust reliable control for a class of uncertain nonlinear state-delayed systems , 1999, Autom..

[80]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[81]  Vadim I. Utkin,et al.  Sliding mode control design principles and applications to electric drives , 1993, IEEE Trans. Ind. Electron..

[82]  Daniel W. C. Ho,et al.  Fuzzy Filter Design for ItÔ Stochastic Systems With Application to Sensor Fault Detection , 2009, IEEE Transactions on Fuzzy Systems.

[83]  Shiuh-Jer Huang,et al.  Adaptive sliding controller with self-tuning fuzzy compensation for vehicle suspension control , 2006 .

[84]  Ian Griffin,et al.  Linear matrix inequalities and evolutionary optimization in multiobjective control , 2006, Int. J. Syst. Sci..

[85]  Timothy Gordon,et al.  A Comparison of Adaptive LQG and Nonlinear Controllers for Vehicle Suspension Systems , 1991 .

[86]  Honghai Liu,et al.  State of the Art in Vehicle Active Suspension Adaptive Control Systems Based on Intelligent Methodologies , 2008, IEEE Transactions on Intelligent Transportation Systems.

[87]  Huijun Gao,et al.  H∞ Fuzzy Control for Systems With Repeated Scalar Nonlinearities and Random Packet Losses , 2009, IEEE Trans. Fuzzy Syst..

[88]  Kisaburo Hayakawa,et al.  Application of H∞ control to active suspension systems , 1994, Autom..

[89]  Hak-Keung Lam,et al.  Stability Analysis and Performance Design for Fuzzy-Model-Based Control System Under Imperfect Premise Matching , 2009, IEEE Transactions on Fuzzy Systems.

[90]  Ismail Yuksek,et al.  LPV gain-scheduling controller design for a non-linear quarter-vehicle active suspension system , 2009 .

[91]  Zehui Mao,et al.  Fault-tolerant control for a class of nonlinear sampled-data systems via a Euler approximate observer , 2010, Autom..

[92]  James Lam,et al.  Non-fragile output feedback H∞ vehicle suspension control using genetic algorithm , 2003 .

[93]  Shengyuan Xu,et al.  Robust H/sub /spl infin// control for uncertain discrete-time-delay fuzzy systems via output feedback controllers , 2005, IEEE Transactions on Fuzzy Systems.

[94]  Rastko R. Selmic,et al.  Actuator fault detection in nonlinear uncertain systems using neural on-line approximation models , 2006, 2006 American Control Conference.

[95]  Shaocheng Tong,et al.  Observer-Based Stabilization of T–S Fuzzy Systems With Input Delay , 2008, IEEE Transactions on Fuzzy Systems.

[96]  R. P. Jones,et al.  Fuzzy logic control of an automotive suspension system , 1995 .

[97]  Xinghuo Yu,et al.  ZOH discretization effect on single-input sliding mode control systems with matched uncertainties , 2009, Autom..

[98]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..

[99]  H. Chen,et al.  Application of Constrained H∞ Control to Active Suspension Systems on Half-Car Models , 2005 .

[100]  Huijun Gao,et al.  Input-Delayed Control of Uncertain Seat Suspension Systems With Human-Body Model , 2010, IEEE Transactions on Control Systems Technology.

[101]  R. A. Williams Electronically controlled automotive suspensions , 1994 .

[102]  Bing Chen,et al.  Reliable control design of fuzzy dynamic systems with time-varying delay , 2004, Fuzzy Sets Syst..

[103]  James Lam,et al.  Stability Analysis and Stabilization for Discrete-Time Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[104]  Lei Zhu,et al.  Modeling of Nonlaminated Electromagnetic Suspension Systems , 2010, IEEE/ASME Transactions on Mechatronics.

[105]  G Chen,et al.  MR damper and its application for semi-active control of vehicle suspension system , 2002 .

[106]  Nurkan Yagiz,et al.  Fuzzy Sliding-Mode Control of Active Suspensions , 2008, IEEE Transactions on Industrial Electronics.

[107]  James Lam,et al.  Semi-active H∞ control of vehicle suspension with magneto-rheological dampers , 2005 .

[108]  Dean Karnopp,et al.  ACTIVE DAMPING IN ROAD VEHICLE SUSPENSION SYSTEMS , 1983 .

[109]  Davor Hrovat,et al.  An approach toward the optimal semi-active suspension , 1988 .

[110]  Huijun Gao,et al.  Robust Sampled-Data Control for Vehicle Active Suspension Systems , 2010 .

[111]  B. R. Davis,et al.  Optimal linear active suspensions with derivative constraints and output feedback control , 1988 .

[112]  Y. Soh,et al.  Reliable H 8 controller design for linear systems , 2001 .

[113]  Marcel Staroswiecki,et al.  Supervisory fault tolerant control for a class of uncertain nonlinear systems , 2009, Autom..

[114]  Huibert Kwakernaak,et al.  Robust control and H∞-optimization - Tutorial paper , 1993, Autom..

[115]  Steven A. Orszag,et al.  Stability and Lyapunov stability of dynamical systems: A differential approach and a numerical method , 1987 .

[116]  Guang-Hong Yang,et al.  State feedback control of continuous-time T-S fuzzy systems via switched fuzzy controllers , 2008, Inf. Sci..

[117]  Xinghuo Yu,et al.  Sliding-Mode Control With Soft Computing: A Survey , 2009, IEEE Transactions on Industrial Electronics.

[118]  Marcel Staroswiecki,et al.  Fault Accommodation for Nonlinear Dynamic Systems , 2006, IEEE Transactions on Automatic Control.

[119]  James Lam,et al.  Multi-objective control of vehicle active suspension systems via load-dependent controllers , 2006 .

[120]  Paul I. Ro,et al.  A sliding mode controller for vehicle active suspension systems with non-linearities , 1998 .

[121]  Jong Hyeon Park,et al.  An H∞ Controlller for Active Suspensions and its Robustness Based on a Full-Car Model , 1999 .

[122]  Ahmad Akbari,et al.  Output feedback H ∞ preview control of active vehicle suspensions , 2008 .

[123]  Zhihong Man,et al.  Non-singular terminal sliding mode control of rigid manipulators , 2002, Autom..

[124]  Nurkan Yagiz,et al.  Sliding mode control of active suspensions for a full vehicle model , 2001 .

[125]  Sing Kiong Nguang,et al.  Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties , 2003 .

[126]  Pierre Apkarian,et al.  Nonlinear H∞ control for an integrated suspension system via parameterized linear matrix inequality characterizations , 2001, IEEE Trans. Control. Syst. Technol..

[127]  Guanghong Yang,et al.  Reliable control using redundant controllers , 1998, IEEE Trans. Autom. Control..

[128]  J. V. Medanic,et al.  On the Design of Reliable Control Systems , 1990, 1990 American Control Conference.

[129]  Stoyan Kamenov Kanev,et al.  Robust fault-tolerant control , 2004 .

[130]  B. R. Davis,et al.  Technical Note: Force Control in Electrohydraulic Active Suspensions Revisited , 2001 .

[131]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[132]  Qing-Long Han A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices , 2005, Int. J. Syst. Sci..

[133]  Johari Halim Shah Osman,et al.  A class of proportional-integral sliding mode control with application to active suspension system , 2004, Syst. Control. Lett..

[134]  Huijun Gao,et al.  Vibration Control of Seat Suspension using H∞ Reliable Control , 2010 .

[135]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[136]  James Lam,et al.  Robust integral sliding mode control for uncertain stochastic systems with time-varying delay , 2005, Autom..

[137]  S. G. Joshi,et al.  OPTIMUM DESIGN OF A PASSIVE SUSPENSION SYSTEM OF A VEHICLE SUBJECTED TO ACTUAL RANDOM ROAD EXCITATIONS , 1999 .

[138]  An-Chyau Huang,et al.  Adaptive sliding control of non-autonomous active suspension systems with time-varying loadings , 2005 .

[139]  Han-Xiong Li,et al.  New Approach to Delay-Dependent Stability Analysis and Stabilization for Continuous-Time Fuzzy Systems With Time-Varying Delay , 2007, IEEE Transactions on Fuzzy Systems.

[140]  Tzuu-Hseng S. Li,et al.  Design of fuzzy controller for active suspension system , 1995 .

[141]  Rajesh Rajamani,et al.  Adaptive observers for active automotive suspensions: theory and experiment , 1995, IEEE Trans. Control. Syst. Technol..

[142]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[143]  Honghai Liu,et al.  Non-fragile H∞ control for half-vehicle active suspension systems with actuator uncertainties , 2013 .

[144]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[145]  Andrew G. Alleyne,et al.  Nonlinear adaptive control of active suspensions , 1995, IEEE Trans. Control. Syst. Technol..

[146]  Michio Sugeno,et al.  An introductory survey of fuzzy control , 1985, Inf. Sci..

[147]  David Crolla,et al.  Road Vehicle Suspension System Design - a review , 1987 .

[148]  Ruey-Jing Lian,et al.  Enhanced fuzzy sliding mode controller for active suspension systems , 2009 .

[149]  Z. Abduljabbar,et al.  LINEAR QUADRATIC GAUSSIAN CONTROL OF A QUARTER-CAR SUSPENSION , 1999 .

[150]  Alessandro Giua,et al.  A Mixed Suspension System for a Half-Car Vehicle Model , 2000 .

[151]  Mehdi Soleymani,et al.  Investigation of the Energy Regeneration of Active Suspension System in Hybrid Electric Vehicles , 2010, IEEE Transactions on Industrial Electronics.

[152]  Shiuh-Jer Huang,et al.  Adaptive fuzzy controller with sliding surface for vehicle suspension control , 2003, IEEE Trans. Fuzzy Syst..

[153]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[154]  Jan A. Snyman,et al.  Optimisation of road vehicle passive suspension systems. Part 1. Optimisation algorithm and vehicle model , 2003 .

[155]  A. J. Healey,et al.  Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles , 1993 .

[156]  Ligang Wu,et al.  Hankel-norm model approximation for LPV systems with parameter-varying time delays , 2010, Int. J. Syst. Sci..