Integral Input to State Stable systems in cascade

The Integral Input to State Stability (iISS) property is studied is the context of nonlinear time-invariant systems in cascade. Some sufficient conditions for the preservation of the iISS property under a cascade interconnection are presented. Those are first given as growth restrictions on the supply functions of the storage function associated to each subsystem, and then are expressed as solutions-based requirements. A Lyapunov-based condition guaranteeing that the cascade composed of an iISS system driven by a Globally Asymptotically Stable (GAS) one remains GAS. Some of these results extend to cascades composed of more than two subsystems.