Abstract
In this chapter, a new frequency-sweeping framework is established, based on its embryonic form proposed in Chaps. 6 and 7. Using this new frequency-sweeping framework, we confirm the invariance property for the most general case. In other words, for any time-delay system with commensurate delays, the invariance property always holds.
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Notes
- 1.
Although \(p(\lambda =0, z=- 0.5 \pm 0.866j)=0\) with \(\left| z \right| = 1\), according to Remark 1.9, \(\lambda =0\) is, however, not a critical imaginary root.
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Li, XG., Niculescu, SI., Çela, A. (2015). A New Frequency-Sweeping Framework and Invariance Property in General Case. In: Analytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays. SpringerBriefs in Electrical and Computer Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-15717-7_8
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DOI: https://doi.org/10.1007/978-3-319-15717-7_8
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Online ISBN: 978-3-319-15717-7
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