The accurate estimation of the State of Charge (SOC) and an acceptable prediction of the Remaining Useful Life (RUL) of batteries in autonomous vehicles are essential for safe and lifetime optimized operation. The estimation of the expected RUL is quite helpful to reduce maintenance cost, safety hazards, and operational downtime. This paper proposes an innovative health-aware control approach for autonomous racing vehicles to simultaneously control it to the driving limits and to follow the desired path based on maximization of the battery RUL. To deal with the non-linear behaviour of the vehicle, a Linear Parameter Varying (LPV) model is developed. Based on this model, a robust controller is designed and synthesized by means of the Linear Matrix Inequality (LMI) approach, where the general objective is to maximize progress on the track subject to win racing and saving energy. The main contribution of the paper consists in preserving the lifetime of battery and optimizing a lap time to achieve the best path of a racing vehicle. The control design is divided into two layers with different time scale, path planner and controller. The first optimization problem is related to the path planner where the objective is to optimize the lap time and to maximize the battery RUL to obtain the best trajectory under the constraints of the circuit. The proposed approach is formulated as an optimal on-line robust LMI based Model Predictive Control (MPC) that steered from Lyapunov stability. The second part is focused on a controller gain synthesis solved by LPV based on Linear Quadratic Regulator (LPV-LQR) problem in LMI formulation with integral action for tracking the trajectory. The proposed approach is evaluated in simulation and results show the effectiveness of the proposed planner for optimizing the lap time and especially for maximizing the battery RUL.