Abstract—This paper deals with the H∞ robust output control for vehicle dynamics where the sideslip angle is unavailable for measurement. This study uses the multiple model approach to represent the vehicle model. The road adhesion conditions change and modeling errors are taking into account by introducing uncertainties. Thus, giving a nonlinear vehicle model, its representation by a multiple model is discussed and validated using vehicle simulator software CarSim. Next, based on the uncertain multiple model of the vehicle, an H∞ controller based on observer is developed. The closed loop stability conditions of a vehicle with the controller and the observer are parameterized in terms of Linear Matrix Inequality (LMI) problem. Numerical simulations of the vehicle handling with the developed observer and controller have been carried out using CarSim simulator. The results obtained indicate that considerable improvements in the vehicle handling can be achieved whenever the vehicle is governed by the proposed H∞ observer-based controller. I. INTRODUCTION HERE is a continuing effort in the automobile industry to achieve the active control systems which improve the stability and the performance of vehicles in dangerous situations [1][2][3][4]. Some of the systems have already been commercialized and been installed in passenger cars (ABS, ESP, TCS ...). However, these systems are still not optimal and they can be improved using an advanced estimation and control design methods [5][6][8][23]. The vehicle safety improvement in terms of stability and comfort achieved by active control systems continues to be a subject of active research [10][11][23]. The ultimate goal is still to produce vehicles that anyone can drive “safely”, “pleasantly” and as one “wishes’’. In this paper, a robust active control with an estimation of the sideslip angle is developed to improve stability and performances of a 4WS vehicle lateral dynamics. The proposed algorithm is based on the multiple model representation largely used in control and estimation prob- M. Chadli, A. El Hajjaji and A. Rabhi are with University of Picardie Jules Verne, Laboratory of "modélisation, Information et Systèmes" EA4290, UPJV-MIS, 7 Rue Moulin neuf, 80000, Amiens, France, (e-mail: {mohammed.chadli, ahmed.hajjaji, abdelhamid.rabhi}@u-picardie.fr) This work was supported by the ”Conseil Régional de Picardie” within the framework of the project ”SEDVAC”. lems of nonlinear systems these last years [13][14][15][17]. The paper is organized as follows. In section 2, we present the vehicle nonlinear model and its representation by a multiple model [18][21]-[24]. The idea is to approximate the system by a convex combination of linear models. The proposed multiple model is validated on CarSim simulator, a software used to simulate and animate dynamic tests of cars [20]. Section 3 presents H∞ robust output control for vehicle dynamics by designing robust observer and controller based on the obtained vehicle multiple models. The design conditions are given in LMI terms [7]. In section 4, simulation results are given to highlight the effectiveness of the design procedure of the observer and the controller and confirm the good performance of the vehicle in dangerous situations (unstable behavior and low road adhesion). Section 5 concludes this paper. II. VEHICLE MODEL DESCRIPTION The two-dimensional model with nonlinear tire characteristics of the four wheels vehicle behavior can be described by differential equations (cf. figure 1) [9][10]: . . 2 2 2 2 f r f f r r z F F r mU aF aF r I + ⎛ ⎞ − ⎛ ⎞ ⎜ ⎟ β ⎜ ⎟ ⎜ ⎟ = ⎜ ⎟ − ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ (1) where β denotes the side slip angle, r is the yaw velocity, F f is the cornering force of the two front tires, F r is the corning force of the two rear tires. U is the vehicle velocity, I z is the yaw moment of inertia, m is the vehicle mass. A. Multiple model representation The cornering forces F f and F r can be approximated as functions of tire slip angles [8]. Here these forces are approximated by multiple model approach as follows ( ) ( ) ( ) ( ) f 1 f f1 f 2 f f2 f r 1 f r1 r 2 f r2 r F = C() + C() F = C() + C() ⎧ µ α µα µ α µα ⎪ ⎨ µ α µα µ α µα ⎪ ⎩ (2) H∞ Observer-based robust multiple controller design for vehicle lateral dynamics M. Chadli, A. El Hajjaji, A. Rabhi T 2010 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 30-July 02, 2010 WeB20.5 978-1-4244-7427-1/10/$26.00 ©2010 AACC 1508