This paper considers both state feedback and dynamic output feedback variable structure control of a nominally linear multivariable system which is affected by disturbances and uncertainties that do not satisfy the matching condition. In order to achieve robust stabilization with respect to the ’residual’ uncertainties and a guaranteed level of rejection of the ’residual’ disturbances during the sliding mode, procedures are proposed whereby the sliding hypersurface is designed using an H-infinity norm-bounding approach. These procedures are illustrated on a two-link flexible joint robot arm example.