Titlebook: Analytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays; Xu-Guang Li,Silviu-Iulian Niculescu,Arben Cela Boo

conspicuous

Invariance Property for Critical Imaginary Roots with Index ,,s by means of the dual Puiseux series, a new concept proposed in this chapter. Then, a useful equivalence relation between the Puiseux series and the dual Puiseux series is found. Based on it, we give a new proof on the invariance property. The aforementioned new perspectives are crucial to confirm the invariance property in the general case.

Delude

Complete Stability for Time-Delay Systems: A Unified Approach,resent the analytical expression of the number of unstable roots. As a consequence, the whole stability domain can be easily obtained by using the frequency-sweeping approach proposed in this book. This is an accurate result, i.e., the system is asymptotically stable if and only if the delay lies in the obtained stability domain.

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Extension to Neutral Time-Delay Systems, the neutral operator. We see that this necessary condition can be embedded in the frequency-sweeping approach, i.e., we may directly verify this condition from the frequency-sweeping curves. Therefore, the complete stability of neutral time-delay systems can be studied within the frequency-sweeping framework.

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Book 2015te delays. The text describes an analytic curve perspective which allows a deeper understanding of spectral properties focusing on the asymptotic behavior of the characteristic roots located on the imaginary axis as well as on properties invariant with respect to the delay parameters. This asymptoti

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Computing Puiseux Series for a Critical Pair, algorithm for calculating all the first-order terms of the Puiseux series. Furthermore, we show that the proposed approach can be used to obtain higher order terms of the Puiseux series in order to study appropriately the degenerate case. Finally, some useful properties on the Puiseux series are presented.

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Hemiplegia

Xu-Guang Li,Silviu-Iulian Niculescu,Arben CelaProposes a simple-to-implement graphical tool for solving complete stability problems without asymptotic behaviour analysis.Completely characterized solution to the open problem of complete stability