Complete controllability
A linear autonomous control system in \({\mathbb{R}}^ n\) is said completely controllable iff there exists \(T>0\) such that each \(x\in {\mathbb{R}}^ n\) can be steered to any \(y\in {\mathbb{R}}^ n\) in time T. This note 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 any \(T>0\), is also derived. This condition generalizes the well known, Kalman condition to the constrained case.
scientific article; zbMATH DE number 3912196