Input-to-State Stability, integral Input-to-State Stability, and   $\mathcal{L}_2$-Gain Properties: Qualitative Equivalences and Interconnected   Systems
  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. 
Christopher M. Kellett and Peter M. Dower
math.OC