Eigenvalues for a nonlinear time-delay system

Abstract

The paper introduces the notion of an eigenvalue of a nonlinear time-delay system. It is shown that the respective object, playing the role of an eigenvalue, is a specific noncommutative polynomial, as it is invariant under a change of coordinates. The basic properties and possible applications of such a formalism are then discussed. Namely, the transformation of a nonlinear time-delay system into the diagonal form.