This paper studies the controller design problem for linear time-invariant systems that have on-off type actuators. Although phase-plane analysis, the describing function approach and pulse-modulation technologies have been studied in the classical literature, such approaches do not permit the direct application of optimal controller design techniques including non-linear effects. In this paper, we propose the application of input-state linearization theory to the general class of single on-off input plants. The linearized space resulting from this method allows the application of any linear controller design tool. The method is also extended to be applicable to on-off controllers with a dead-band. To demonstrate the effectiveness of this approach, some numerical studies are presented including the lunar landing problem, and the results are evaluated and compared with numerical optimal solutions.