  In systems where the ability to actuate is a scarce resource, e.g.,
spacecrafts, it is desirable to only apply a given controller in an
intermittent manner--with periods where the controller is on and periods where
it is off. Motivated by the event-triggered control paradigm, where
state-dependent triggers are utilized in a sample-and-hold context, we
generalize this concept to include state triggers where the controller is off
thereby creating a framework for intermittent control. Our approach utilizes
certificates--either Lyapunov or barrier functions--to design intermittent
trigger laws that guarantee stability or safety; the controller is turned on
for the period for which is beneficial with regard to the certificate, and
turned off until a performance threshold is reached. The main result of this
paper is that the intermittent controller scheme guarantees (set) stability
when Lyapunov functions are utilized, and safety (forward set invariance) in
the setting of barrier functions. As a result, our trigger designs can leverage
the intermittent nature of the actuator, and at the same time, achieve the task
of stabilization or safety. We further demonstrate the application and benefits
of intermittent control in the context of the spacecraft orbit stabilization
problem.
