Nonlinear Behavioral Balancing by Extension of Lie Semigroups

Previously, a balancing condition for nonlinear systems was introduced. This paper provides an extended justification of such balancing condition in terms of semigroups of diffeomorphisms in a Hilbert submanifold framework. Moreover, it is argued that when such condition is satisfied the resulting group of diffeomorphisms describes the flow of the nonlinear system. Using the same framework the nonlinear behavioral operator is defined and a result regarding its spectral properties is presented.