Relationships Between Subclasses of Integral Input-to-State Stability

A certain “qualitative equivalence” has been recently demonstrated between integral input-to-state stability (iISS) and a nonlinear L
₂
-gain property. Furthermore, it has been observed that the properties of strong iISS and nonlinear 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 L
₂
-gain properties.