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The paper is concerned with a class of time-delay systems that are linearly equivalent to higher-order scalar equations. If the retarded case was considered some four decades ago in Halanay (1969), the non-trivial neutral case is considered here. The specific structure of these systems endows them with remarkable properties that are useful in various applications in dynamics and control. As an auxiliary necessary result, the variation of parameters formula is revisited what opens new perspectives for research progress in such directions as the Perron condition and forced linear oscillations. [ABSTRACT FROM PUBLISHER]

This paper focuses on Forced oscillations (periodic and almost periodic) in some dynamical models described by coupled differential and difference equations. The existence and stability result is based on a theorem on invariant manifolds on Banach spaces due to Kurzweil and Halanay. The state‐space (based on Liapunov–Krasovskii functionals combined with the S‐procedure) approach is considered. An illustrative example is presented and some conclusions are drawn concerning sharpness and ease in applications of the method. [ABSTRACT FROM PUBLISHER]