This thesis deals with design techniques for robust non-linear multivariable systems. It describes and discusses some design techniques for such systems. First, one-loop-at-a-time design using the root locus method is considered. The disadvantages of this approach are outlined. Next, some gain-schedulmg controllers are designed for each loop. Then, a multivariable optimization approach is taken. Software to find the frequency domain solution of the two-block weightedmixed- sensitivity problem using the Youla Parameterisation and Smith-McMillan form is developed. This two-variable problem decouples into two single-variable problems, corresponding to optimizing at the input and output of the plant. The fundamental limitations and the trade-offs in design are studied at the input and output of the plant. A11 controllers are tested and implemented on the inverted pendulum-cart apparatus, an unstable single-input two-output system.