A geometric approach to nonlinear dissipative balanced reduction I: exogenous signals

This paper is divided into two parts and provides a unified geometric theory for nonlinear dissipative and Hankel balanced reduction with the help of a framework based on differential geometry, dissipativity theory, Lie-semigroups and sub manifold Hilbert theory. Part I presents a theory for the invariants of the behavior using classical Gauss’ curvature theory. Furthermore, known concepts of the theory of balanced reduction like the Hankel operator, Schmidt decomposition, etc., can be understood in a proper and general perspective.