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Time-delay systems with remarkable structural properties. (English) Zbl 1251.93036

Summary: 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.

MSC:

93B05 Controllability
93C15 Control/observation systems governed by ordinary differential equations
34H05 Control problems involving ordinary differential equations
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