This paper studies the minimum switching control problem for a system of coupled double integrators with on-off input signals, in the presence of a constant disturbance term. This type of problem is relevant to a variety of applications in which the number of transitions of on-off actuators must be minimized, in order to prevent actuator wear. Two solutions are presented in terms of steady state limit cycles. The first one provides an analytic upper bound to the maximum number of transitions per input signal. The second solution exploits the relative phases of the trajectories of the state variables, thus providing a less conservative upper bound. Additionally, a control law is presented, which steers the system in finite time to the previously derived limit cycles. The proposed techniques are demonstrated on a spacecraft attitude control application. (C) 2015 Elsevier Ltd. All rights reserved.