I'm following two timeseries: one is a setpoint, the other is the controlled output. When the setpoint rises I want the controlled output to follow quickly; when the setpoint drops, it's acceptable to have the output drop more slowly.
Is there a metric that can quantify this behaviour? Some kind of "positive cross-correlation"?
Here is a plot of the two signals I'm following. The red line is the setpoint, the orange line is the output signal.