论文标题
单层线性方程的复合根的光谱优势
Spectral dominance of complex roots for single-delay linear equations
论文作者
论文摘要
本文为存在一对复杂的共轭根提供了必要和充分的条件，而在线性时间不变的单层延迟类型的单程中，每个多重性二的根部都提供了必要的条件。这对根也被证明始终是严格的主导性，因此确定了系统的渐近行为。该结果的证明是基于多样性的真实根的相应结果，与参数相对于参数的连续依赖性以及对越过虚基根的研究。我们还介绍了如何将这种设计应用于振动抑制和柔性模式补偿。
This paper provides necessary and sufficient conditions for the existence of a pair of complex conjugate roots, each of multiplicity two, in the spectrum of a linear time-invariant single-delay equation of retarded type. This pair of roots is also shown to be always strictly dominant, determining thus the asymptotic behavior of the system. The proof of this result is based on the corresponding result for real roots of multiplicity four, continuous dependence of roots with respect to parameters, and the study of crossing imaginary roots. We also present how this design can be applied to vibration suppression and flexible mode compensation.
