Eigenvalues and poles of nonlinear systems: A geometric approach

The classical notions of eigenvalue and of pole of a linear system are revisited using a geometric approach and extended to nonlinear systems exploiting the notions of f - reducing manifold and of f-reducing distribution. The proposed definitions contribute to a deeper understanding of the model reduction problem at isolated singularities, recently studied in a companion paper by the authors, and may prove useful in the solution of stabilization problems for nonlinear systems. Simple worked-out examples illustrate the theory.