We consider the problem of controlling the dynamic state of each of a finite collection of targets distributed in physical space using a much smaller collection of mobile agents. Each agent can attend to no more than one target at a given time, thus agents must move between targets to control the collective state, implying that the states of each of the individual targets are only controlled intermittently. We assume that the state dynamics of each of the targets are given by a linear, time-invariant, controllable system, and develop conditions on the visiting schedules of the agents to ensure that the property of controllability is maintained in the face of the intermittent control. We then introduce constraints on the magnitude of the control input and a bounded disturbance into the target dynamics and develop a method to evaluate system performance under this scenario. Finally, we use this method to determine how the amount of time the agents spend at a given target, before switching to the next in its sequence, influences the control of the states of the entire collection of targets.