In recent years there has been growing interest in the descriptive analysis of l-order time invariant linear dynamical system xl = Al-1xl-1 ++ A0x0 where Ai are square complex matrices and xi denotes the i-th derivative of x. We are interested to mesure the minimum number of controls B that are needed in order to make the system xl = Al-1xl-1 ++ A0x0 + Bu controllable.