Establishing iISS Property of Interconnected Systems via Parametrization of Supply Rates

This paper deals with the problem of establishing integral Input-to-State Stability(iISS) of interconnected nonlinear systems. Recently, the iISS-ISS small-gain theorem has been developed to cover iISS components to which the popular ISS small-gain theorem is not applicable. This paper focuses on a small-gain-like ‘condition´ in the iISS-ISS small-gain `theorem’. The purpose is to expand the capability of the iISS-ISS small-gain `condition´ by introducing new flexibility in choosing supply rates. A novel technique of parametrization of supply rates provides us with many supply rates with which a fixed single iISS-ISS small-gain condition can establish the iISS property of the interconnection.