Ito, Hiroshi (Kyushu Inst. of Tech.)

A Generalized Small-Gain Formula for Nonlinear Interconnected Systems: An Equivalent of iISS-ISS Small-Gain Condition

Scheduled for presentation during the Regular Session "Nonlinear Control II" (ThP05), Thursday, July 27, 2006, 15:45−16:10, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

This paper discusses stability conditions for establishing integral input-to-state stability of interconnected systems. Feedback connection of an iISS(integral input-to-state stable) system and an ISS(input-to-state stable) system is investigated. Recently, the iISS-ISS small-gain theorem has been developed to address the problem and provided a sufficient condition. This paper shows that the iISS-ISS small-gain condition can be replaced by a much simpler formula which is practically more attractive. It only requires a mild assumption about differentiability of functions composing supply rates of systems. The generalized small-gain formula proposed in this paper is an alternative representation of a popular nonlinear small-gain condition for ISS systems. Thus, this paper demonstrates that stability of interconnected ISS systems and interconnected iISS systems can be established by exactly the same universal condition.