Relaxing growth rate assumption for integral input-to-state stability of cascade systems

This paper addresses stability criteria for cascaded nonlinear systems. A stability criterion which a preceding study reported to relax a growth rate assumption is reviewed. Through presentation of its proof which was omitted in publication of the preceding study, this paper demonstrates that careful examination of the proof leads to several new extensions allowing disturbance inputs which were not allowed by the preceding result. Numerical simulation is shown to illustrate the mechanism and usefulness of the new criteria.