The sliding-mode control approach is developed for a class of discrete-state systems in a metric space. A concept of trajectory continuity is introduced which allows the use of sliding-mode design techniques similar to that in continuous state systems, This approach is then applied to a class of hybrid systems which consists of a continuous plant, an interface, and a discrete-state controller. The introduction of the sliding-mode concept leads to a design which is invariant to disturbances and also the solution of the stabilization problem.