The almost-complete controllability of a linear stationary system (Q1821065)

Given are a linear system (*) \(\dot x=Ax+Bu\) and a subspace \(G=\{x:\) \(Hx=0\}\), where A, B, H are constant matrices of dimensions \(n\times n\), \(n\times r\) and \(m\times n\) respectively. The goal is to find necessary and sufficient conditions for controllability of system (*) with reference to G. The paper shows that the system can be brought from almost each \(x_ 0\in E^ n\) (but not from each) to G. Moreover, the paper deals with necessary and sufficient conditions for controllability of system (*) with reference to both the subspace G and the hyperplane \(\tilde G=G+d\) where d is a fixed vector in \(E^ n\). The controls u(t) bringing the system (*) from \(x_ 0\in E^ n\) to G are defined.