In this paper, an innovative health-aware control approach is presented for autonomous racing vehicles. Based on a dynamical model of the vehicle, a controller is computed by means of the Linear Matrix Inequality (LMI), 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 state of charge (SoC) and optimizing a lap time to achieve the best path of a racing vehicle. The control design is divided into two parts, path planner and controller. The first optimization problem is related to the path planner where the objective is to optimize the lap time and maximize the SoC to obtain the best trajectory under the constraints of the circuit. The proposed optimization problem is solved by LMI based Model Predictive Control (MPC) driven from Lyapunov stability. The second part is focused on a controller gain synthesis solved by LMI formulation with integral action for tracking the trajectory obtained from the planner part. The proposed optimizations problem is evaluated in simulation and results show the effectiveness of the proposed planner for optimizing the lap time and especially for maximizing the SoC of the battery.