A geometric approach to nonlinear dissipative balanced reduction II: internal isometries

Abstract

This Part II provides structural aspects of the internal signals and operators used in the unified geometric theory for nonlinear dissipative and Hankel balanced reduction using the differential-geometric framework based on dissipativity theory, Lie-semigroups and submanifold Hilbert theory. In particular, a novel characterization of the nonlinear Gramians is presented along with an alternative view of some concepts of the theory of nonlinear balanced reduction and the Hankel operator, namely eigenvalue problems and eigenfunction decomposition, etc.