This note gives results about the preservation of some dissipative properties of systems under a change of
variables. In the textbooks it is not mentioned explicitly the relationship between the equations associated with the
dynamics of a system and the selected Lyapunov function to establish its stability property, when a change of coordinates
is used. Based on the fact that Lyapunov stability is preserved under these changes of variables, it is shown that various
forms of dissipativity can be preserved. In addition, we will show that the input-state stability (ISS), integral input-to-state
stability (iISS) and input/output to state stability (IOSS) can be preserved under this class of transformation. Some
examples are given to show these results.