Permanent magnet synchronous motor-powered electric vehicles control is the subject of various research work. However, their global dynamic models are nonlinear and coupled. Therefore, to achieve efficient operation, an effective control system is crucial. In this study, we propose and compare linear H-Infinity and Galerkin approximation approach for Nonlinear H-Infinity control strategies to improve the durability and performance of post-driven speed in electric vehicles. In the case of linear systems, the linear H-Infinity controller is found by solving the algebraic equation known as the Riccati equation. On the other hand, the control problem based nonlinear H-Infinity poses challenges because it involves solving a nonlinear partial differential equation known as name of the Hamilton-Jacobi-Isaacs equation, which is difficult or even impossible to solve by using analytical methods. In these situations, the Galerkin approximation approach provides an approximation to the Hamilton-Jacobi equation solution. In order to evaluate the performance of Galerkin approximation approach and linear H-Infinity controllers, electric vehicle feedback simulations will be conducted, taking into account different constraints. The goal is to ensure efficient operation in different situations. The results demonstrate that the Galerkin approximation Approach for nonlinear H-Infinity controller reveals a similar performance and durability as the H-Infinity controller, and stands out for its ability to optimize the control system performance of the EV, providing a faster response, reducing undesirable ripples, and enhancing overall stability and precision. Generally, this comparative study brings to light the effectiveness of linear and Galerkin approximations for H-Infinity control in permanent magnet synchronous motor-powered electric vehicles. The results contribute to the advancement of control strategies and provide valuable information for the conception and employment of efficient electric vehicle control systems.