*Article* **Active Suspension Control Using an MPC-LQR-LPV Controller with Attraction Sets and Quadratic Stability Conditions**

**Daniel Rodriguez-Guevara 1, Antonio Favela-Contreras 1,***∗***, Francisco Beltran-Carbajal 2, David Sotelo <sup>1</sup> and Carlos Sotelo <sup>1</sup>**


**Abstract:** 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 Inequalities (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.

**Keywords:** active suspension; model predictive control; linear parameter varying; ellipsoidal set; attraction sets; quadratic stability
