The control of an automotive suspension system by means of a hydraulic actuator is a complex nonlinear control problem. In this work, a Linear Parameter Varying (LPV) model is proposed to reduce the complexity of the system while preserving the nonlinear behavior. In terms of control, a dual controller consisting of a Model Predictive Control (MPC) and a Linear Quadratic Regulator (LQR) is implemented. To ensure stability, Quadratic Stability conditions are imposed in terms of Linear Matrix

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... ualities (LMI). Simulation results for quarter-car model over several disturbances are tested in both frequency and time domain to show the effectiveness of the proposed algorithm.