  Input-to-state stability (ISS) and $\mathcal{L}_2$-gain are well-known robust
stability properties that continue to find wide application in the analysis and
control of nonlinear dynamical systems and their interconnections. We
investigate the relationship between ISS-type and $\mathcal{L}_2$-gain
properties, demonstrating several qualitative equivalences between these two
approaches. We subsequently present several new sufficient conditions for the
stability of interconnected systems derived by exploiting these qualitative
equivalences.
