The notion of input-to-state stability (ISS) has proved to be useful i
n nonlinear systems analysis. This paper discusses a dual notion, outp
ut-to-state stability (OSS). A characterization is provided in terms o
f a dissipation inequality involving storage (Lyapunov) functions. Com
bining ISS and OSS there results the notion of input/output-to-state s
tability (IOSS), which is also studied and related to the notion of de
tectability, the existence of observers, and output injection.