Stability criteria for interconnected iISS systems and ISS systems using scaling of supply rates

This paper deals with problems of stability analysis of feedback and cascade interconnection of dissipative nonlinear systems. The purpose is to establish stability of systems having more general and stronger nonlinearity than systems considered by classical small-gain theorems and modern stability criteria such as the ISS small-gain theorem. This paper employs a unique idea of "state-dependent scaling of supply rates" to achieve the goal. Novel techniques to manipulate scaling functions are developed, and they play a key role in establishing stability for broader classes of systems. One of important results is a small-gain theorem for feedback interconnection of integral input-to-state stable (iISS) systems. The results not only demonstrate applicability to general systems, but also substantiate the effectiveness and usefulness of the state-dependent scaling in obtaining solutions successfully for classes of systems broader than input-to-state stable (ISS) systems.