A note on representation of nonlinear time-varying delay-differential equations as time-delay feedback systems

Abstract

This paper is concerned with the relationship between delay-differential equations (DDEs) and time-delay feedback systems, and studies the conversion problem of nonlinear time-varying (NLTV) DDEs into representations as time-delay feedback systems, i.e., NLTV systems in feedback connection with pure delays. We first introduce adequate definitions of the solutions of the initial value problems for DDEs under possibly discontinuous initial functions, together with appropriate assumptions for ensuring the global existence and uniqueness of such solutions. We then tackle the conversion problem and solve it including the conversion of initial conditions, and discuss the relation of the conversion method with an existing result confined to linear time-invariant DDEs.