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

MTNS 2006 Paper Abstract


Paper TuP05.5

Ito, Hiroshi (Kyushu Inst. of Tech.)

Parametrization of Supply Rates for Multi-Loop ISS Systems: Beyond Invariance of Nonlinear Gain

Scheduled for presentation during the Regular Session "Nonlinear Control I" (TuP05), Tuesday, July 25, 2006, 17:00−17:25, 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 27, 2023

Keywords Stability analyisis, Uncertain systems, Large scale systems


This paper concerns input-to-state stability(ISS) of nonlinear interconnected systems consisting of multiple individually-ISS subsystems. This paper focuses on ``parametrization of supply rates'' which is a tool proposed recently by the author for selecting supply rates leading to the stability of interconnected systems successfully. The purposes of this paper are two-fold. One is to present a new interpretation of the parametrization. An invariance property of nonlinear gain under parametrization is proved, which provides a new proof of the parametrization for single-loop systems. The other is to develop the parametrization for multi-loop systems. The invariance is valid only for single-loop systems. For multi-loop systems, we are not able to resort to the invariance property. The parametrization for multi-loop systems is considered as natural generalization of a popular linear tool called scaled H infinity criteria to nonlinear systems. Nonlinear gain and ISS property this paper employs are much more suitable than H infinity norm and finite H infinity property. In contrast to linear systems, the technique of parametrization is indispensable for nonlinear systems even in the single-loop case. The usefulness is explained from an inverse optimal perspective.