Characterizations of output controllability for LTI systems

The objective of this paper is to make, in a simple and rigorous way, some contributions the notion output controllability. We first examine, for general linear time-invariant systems, state controllability, introduced 60s by Bertram Sarachik. More precisely, we extend Hautus test, well-known case propose controllability Gramian matrix, allowing us build continuous control achieving transfer with minimal energy. also give two other notions namely globally For each these new notions, necessary sufficient conditions, terms Kalman rank, test matrices.