This work investigates the H∞ optimal controller design for a fractional order system with time delay. For illustrative purposes, a magnetic suspension system model, derived by Knospe and Zhu is considered. The transfer function is infinite dimensional including e −hs and a rational function of √ s, where h > 0 represents the delay. Recently in a paper by Ozbay, a formulation is given to design the ¨ H∞ optimal controller for the mixed sensitivity minimization problem for unstable infinite dimensional plants with low order weights. This formulation is used to design the H∞ optimal controller for the fractional order system considered, and it is compared to alternative computation methods for H∞ control of infinite dimensional systems. To implement the controller, approximation methods are also investigated. Furthermore, finite dimensional rational approximation techniques of the fractional order integrator are evaluated for simulation purposes.