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

Input-to-State Stability, integral Input-to-State Stability, and  $\mathcal{L}_2$-Gain Properties: Qualitative Equivalences and Interconnected  Systems