This thesis deals with the modern control approaches applicable to speed control of an induction motor. Historical perspective to the control theory and its evolution to the modern control will be presented in a short introduction. Basics of uncertainty modeling are presented along with linear fractional transformation (LFT) representation of an uncertain system. Two different approaches for robust controller synthesis are introduced - H-infinity loopshaping and mixed sensitivity H-infinity synthesis. Theoretical background is presented for both of these methods. Finally the robust controller for induction motor satisfying the control goals is designed using both methods. Design objectives are presented as transfer function weights shaping the sensitivity or complementary sensitivity function to desired shape. Several step responses were simulated to compare H-infinity loopshaping and mixed sensitivity H-infinity controllers with the conventional vector control approach.