  This paper aims at formulating definitions of topological stability,
structural stability, and expansiveness property for an iterated function
system( abbrev, IFS). It is going to show that the shadowing property is
necessary condition for structural stability in IFSs. Then, it proves the
previous converse demonstration with the addition of expansiveness property for
IFSs. It asserts that structural stability implies shadowing property in IFSs
and presents an example to reject of the converse assertion.
