Controllability and observability of linear systems: some noninvariant aspects

Most textbooks in linear systems present controllability and observability as being invariant under coordinate transformations. Although this concept is correct from a certain viewpoint, in a more general sense it could be misleading. This latter viewpoint is not usually emphasized in basic courses and the gap left has often proved to be difficult for students to overcome. This paper addresses both viewpoints and special attention is devoted to the one which is often neglected. The controllability/observability of transfer functions is also discussed and important links with the state space representation are pointed out