This paper presents the design and evaluation of a Linear Time-Varying Linear Quadratic Gaussian (LTV-LQG) controller for an energy efficient electric vehicle, using a predetermined driving strategy as the reference trajectory. The proposed approach begins with the development of a structured nonlinear vehicle model based on relevant subsystems, enabling accurate energy consumption estimation with a deviation of less than 2% from experimental measurements. This model serves as the basis for computing a near-optimal driving trajectory. The nonlinear model is linearized along the predefined trajectory to support control design. A time-varying control structure is then developed, integrating a Kalman filter that estimates unmeasured external disturbances, such as wind, and enhances feedback performance. The proposed control strategy is evaluated through simulations and compared to a rule-based switching controller that replicates human-like driving behavior. The simulation results demonstrate that the LTV-LQG controller consistently satisfies the time constraints in both headwind- and tailwind-dominant scenarios, where the switching controller tends to exceed the time limit. Moreover, in tailwind-dominant cases, the LTV-LQG controller achieves lower energy consumption (up to 15.4%). The proposed framework represents a computationally efficient and practically feasible control solution for electric vehicles operating under realistic disturbance conditions.