A pneumatic actuator with solenoid valves is a discontinuous-input system because each valve can be either in on or off state. For such an actuator, this paper proposes a sliding- mode control scheme that is based on an averaged continuous- input model of the discontinuous-input open-loop system. The averaged model is obtained from the nonlinear dynamics of the open-loop system undergoing pulse-width-modulation (PWM) at the input (i.e., valve open/close action). The PWM duty cycle will be regarded as a continuous input to the proposed averaged model, and thus generated by the proposed sliding- mode controller. For the sliding control design, we note that a pneumatic actu- ator has two chambers with a total of four on/off valves. Thus, there are sixteen possible combinations for valves' switching. Seven of these sixteen operating "modes" are considered both functional and unique. The proposed sliding control utilizes and switches between these seven modes of the open-loop system in order to select the ones with necessary and sufficient amounts of drive energy. In comparing the new 7-mode controller to the previous controllers, we will demonstrate reductions in the position tracking error and the number of switches made by the actuator's on/off valves. The proposed control scheme is used in both position control of a pneumatic cylinder and bilateral control of a one degree of freedom teleoperation system. Experimental results are presented to validate our theoretical findings.