A new formulation of small-gain theorem without imposing strong iISS with respect to Disturbances on components

The small-gain paradigm has long been used to verify stability of feedback interconnected systems. For component systems that are integral input-to-state stable (iISS), available small-gain results require the component systems to be strongly iISS. We remove this restriction by using a recently proposed Lyapunov characterization of iISS that allows cross terms between external inputs and states in the Lyapunov decrease condition. This novel formulation extends previously available iISS small-gain arguments, which is demonstrated in an example.

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