Improved results of changing supply functions and the applications to nonlinear systems in cascade

This paper addresses the problem of changing supply functions in nonlinear systems. A dissipation inequality for the derivative of a storage function is introduced to describe the behavior of the systems. The dissipation inequality is allowed to hold only in a compact set and/or with some bounded functions. Then the results on modifying the involved functions are provided. Moreover, the obtained results are applied to the cascaded integral input-to-state stable systems. It is showed that, by some proper assumptions on the functions of dissipation inequality, the integral input-to-state stability of the cascaded systems could be inherited from the property of each subsystem.