Discussion on: "On a Small Gain Theorem for ISS Networks in Dissipative Lyapunov Form"

In the paper by Dashkovskiy, Ito, and Wirth the construction of Lyapunov functions for nonlinear composite systems is pursued. These systems consist of usually more than two interconnected subsystems for which input-to-state stability (ISS) Lyapunov functions are assumed to be known. Yet, so far, the stability of the overall system, or equivalently, the existence of a Lyapunov function for the composite system is not guaranteed. Instead, a sufficiency condition which generalizes the well known small-gain condition