Summary
International Symposium on Nonlinear Theory and its Applications
2005
Session Number:3-1-1
Session:
Number:3-1-1-6
Stability of Dissipative Interconnections
Kiyotsugu Takaba, Jan C. Willems,
pp.695-698
Publication Date:2005/10/18
Online ISSN:2188-5079
Summary:
This paper is concerned with the stability analysis of the interconnection of two systems. The idea is that, under suitable assumptions, the interconnection of dissipative systems is Lyapunov stable. This is the basis of the classical stability criteria such as the small gain theorem, the positive operator theorem, IQC’s, etc. In terms of quadratic differential forms, this paper derives stability conditions for the interconnection consisting of a linear time-invariant subsystem and a general (nonlinear, timevarying) subsystem in the general setting where the supply rate is induced by a polynomial or rational matrix.