A Universal Parametrization of Supply Rates for iISS and ISS Systems

This paper is concerned with the development of a new tool for establishing stability of interconnected nonlinear systems. The purpose is to accomplish continuous generalization of "parametrization of supply rates" developed previously for ISS systems to cover a broader class of systems characterized by integral input-to-state stability (iISS) property. Recently, a primary attempt has been made to expand the framework of parametrization to iISS systems. However, the primary result looks too restrictive to be used in practice since it involves a complicated gain condition and requires additional restrictions compared with the ISS case. This paper removes all the restrictions and simplifies the gain condition. A universal formula is proposed for the parametrization which is applicable to iISS systems as well as ISS systems in a unified manner