Sampling frequency and controllability region

In order to decide on the sampling frequency in a digital control system, a measure V is introduced for the subset of states, which can be transferred to the origin within a given time interval θ by a constrained control input. V increases with the number N of samplings in the interval θ = NT, but at the same time the required computer time increases. It is shown, how V(T) can be computed for multi-variable systems. A plot of V(T) allows a trade-off between controllability region and computer time by choice of the sampling interval T.