[6][7] The proportionality factor in the definition of Ross' time constant is dependent upon the magnitude of the disturbance on the plant and the specifications for feedback control.
Ross et al showed that this time constant is connected to the practical implementation of a Caratheodory-π solution.
[6] That is, Ross et al showed that if feedback solutions are obtained by zero-order holds only, then a significantly faster sampling rate is needed to achieve controllability and stability.
On the other hand, if a feedback solution is implemented by way of a Caratheodory-π technique, then a larger sampling rate can be accommodated.
These concepts have been used to generate collision-avoidance maneuvers in robotics in the presence of uncertain and incomplete information of the static and dynamic obstacles.