This paper analytically derives the bandwidth limitations of Disturbance Observer (DOB) when plants have Right Half Plane (RHP) zero(s) and pole(s). If the plant is non-minimum phase, then the bandwidth of DOB should be set at a lower value than its upper bound to improve the robust stability and performance. If the plant is unstable, then the bandwidth of DOB should be set at a higher value than its lower bound to achieve the robust stability. The upper and lower bounds are analytically derived by using Poisson integral formula. It is shown that the bandwidth limitation of DOB is directly related to the locations of the RHP zero(s) and pole(s) and becomes more severe as they get close each other. A minimum phase approximation of the non-minimum phase nominal plant model is proposed by using Genetic Algorithm (GA) to tackle the internal stability problem of the DOB-based robust control systems. Simulation results are given to verify the proposed robust controllers.