Complete controllability

A linear autonomous control system in ⁿ is said to be completely controllable iff there existsT>0 such that eachx ⁿ can be steered to anyy ⁿ in timeT. This paper presents a geometric characterization of this property in the case in which there are constraints on the values which the control maps can assume. A necessary and sufficient condition to get instant controllability (i.e., complete controllability for anyT>0) is also derived. This condition generalizes the well-known Kalman condition to the constrained case.