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.