  For an ISS system, by analyzing local and non-local properties, it is
obtained different input-to-state gains. The interconnection of a system having
two input-to-state gains with a system having a single ISS gain is analyzed. By
employing the Small Gain Theorem for the local (resp. non-local) gains
composition, it is concluded about the local (resp. global) stability of the
origin (resp. of a compact set). Additionally, if the region of local stability
of the origin strictly includes the region attraction of the compact set, then
it is shown that the origin is globally asymptotically stable. An example
illustrates the approach.
