How violent are fast controls? .2.

For a linear autonomous system, if a state is reachable from zero in some time duration, then it is reachable within any positive time duration. However, the norm of the control that steers the zero state to the given reachable state increases as the available control time shrinks. This paper gives the asymptotics of minimal L-p-norm controls as the time duration goes to zero; there are also some further remarks for other related norms.