Global controllability of linear autonomous systems: a geometric consideration (Q1061060)

Let \(\dot x=Ax+u\) be a linear control system in \({\mathbb{R}}^ n\). The values of the controls u are constrained to belong to a non empty subset C of \({\mathbb{R}}^ n\). In this paper the author proves necessary conditions and sufficient conditions in order that a system locally controllable at 0 will be globally controllable at 0. The conditions are based on geometric considerations and involve the eigenvectors of A, the transposed matrix of A and the recession cone of C.