  This paper deals with several related notions of output stability with
respect to inputs. The inputs may be thought of as disturbances; when there are
no inputs, one obtains generalizations of the classical concepts of partial
stability. The main notion studied is called input to output stability (IOS),
and it reduces to input to state stability (ISS) when the output equals the
complete state. Several variants, which formalize in different manners the
transient behavior, are introduced. The main results provide a comparison among
these notions. A companion paper establishes necessary and sufficient
Lyapunov-theoretic characterizations.
