Are there theories to manage states of signal volatility around a limit

Assume input signal and discrete output. The signal can cross the limit at 1000 times per second, but it is desired that the discrete output changes at the most once every 15 seconds. See image below:

$U$ is the Signal, $A$ is the comparator output, $B$ is the filtered output. The goal is to filter out the output changes in region $R$.

• Are there theories to dealing with volatility around the limit such as in region $R$ ?

• At this point I am thinking of an algorithm where state is only changed if the signal is persistent for time period $T$, is there a name for such an algorithm?

• Do you mean that the state of the system determines the which dynamics is used? So for example $\dot{x}=Ax+Bu$ and $u=\max(-1,\min(Kx,1))$. May 23 '16 at 23:40
• Actually the other way around, want to reduce frequent changes of state due to volatile signal. The signal can cross the warning limit at kHz, but the state should only change from normal to warning and vise versa at most one per 15 sec. May 24 '16 at 0:03