A parametrization of supply rates for small-gain conditions for global stability of interconnected iISS and ISS systems

This paper develops a novel tool of establishing global asymptotic stability of nonlinear interconnected systems. The aim is to incorporate useful flexibility in small-gain techniques for integral input-to-state stable (iISS) and input-to-state stable (ISS) systems. This paper introduces a unique idea of "parametrization of supply rates", which parametrizes a set of many supply rates with which stability of an interconnected system can be derived from a single small-gain condition. The parametrization offers convenient flexibility of free functions to determine proper supply rates that match systems and that lead to stability of the interconnection. The new parametrization covers iISS systems as well as ISS systems.