LAUSR

A certain “qualitative equivalence” has been recently demonstrated between integral input-to-state stability (iISS) and a nonlinear $\mathcal{L}_2$ -gain property. Furthermore, it has been observed that the properties of strong iISS and nonlinear $\mathcal{L}_2$-gain are preserved when multiple systems satisfying the respective property are connected in cascade. This technical note clarifies the relationships between various input-to-state stability and (non)linear $\mathcal{L}_p$ -gain properties.