Unidentifiability versus "actual" observability

It is shown that the observability of a linear state equation, only input-output accessible, does not imply that all the states can be actually evaluated. Such possibility, depends on the identifiability properties of the equations. A necessary, and sufficient condition for observability of the states, when the equations are unidentifiable, is derived. It is also shown that in such situations the "actual" observability\´ may depend also on the input matrix.