A new methodology is presented for assessing the stability posture of a general class of linear time-invariant—neutral time-delayed systems (LTI-NTDS). It is based on a “Cluster Treatment of Characteristic Roots CTCR” paradigm, which yields a procedure called the Direct Method (DM). The technique offers a number of unique features: It returns exact bounds of time delay for stability, as well as the number of unstable characteristic roots of the system in an explicit and nonsequentially evaluated function of time delay. As a direct consequence of the latter feature, the new methodology creates entirely, all existing stability intervals of delay, . It is shown that the Direct Method inherently enforces an intriguing necessary condition for -stabilizability, which is the main contribution of this paper. This, so-called, “small delay” effect, was recognized earlier for NTDS, only through some cumbersome mathematics. Furthermore, the Direct Method is also unique in handling systems with unstable starting posture for , which may be -stabilized for higher values of delay. Example cases are provided.
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March 2005
Technical Papers
The Cluster Treatment of Characteristic Roots and the Neutral Type Time-Delayed Systems
Rifat Sipahi
Rifat Sipahi
University of Connecticut
, Mechanical Engineering Department, Storrs, CT 06269-3139
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Nejat Olgac
ASME Fellow
Rifat Sipahi
University of Connecticut
, Mechanical Engineering Department, Storrs, CT 06269-3139J. Dyn. Sys., Meas., Control. Mar 2005, 127(1): 88-97 (10 pages)
Published Online: March 27, 2004
Article history
Received:
September 18, 2003
Revised:
March 27, 2004
Citation
Olgac, N., and Sipahi, R. (March 27, 2004). "The Cluster Treatment of Characteristic Roots and the Neutral Type Time-Delayed Systems." ASME. J. Dyn. Sys., Meas., Control. March 2005; 127(1): 88–97. https://doi.org/10.1115/1.1876494
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