A well-known robust observer-based sliding-mode output tracking control developed for strictly proper, minimum phase systems is extended to the control of relative degree zero, MIMO non-minimum phase plants. By assuming that the class of uncertainty is limited to an appropriate sub-space of the actuator range-space, a sliding-mode tracking control for non-minimum phase systems is posed. By introducing some dynamics, in the form of a plant output filter, relative degree zero plants are proved to be robustly controllable. The design of the linear components of the tracking control and the observer gains is posed in an H-2-framework. The control law is exemplified on the control of a highly non-linear, benzene producing, large scale chemical process.