Search

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