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Research Papers

Investigation of Local Stability Transitions in the Spectral Delay Space and Delay Space

[+] Author and Article Information
Qingbin Gao

Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: qingbin.gao@uconn.edu

Umut Zalluhoglu

Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: umut.zalluhoglu@uconn.edu

Nejat Olgac

Fellow ASME
Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: olgac@engr.uconn.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 3, 2013; final manuscript received March 3, 2014; published online June 12, 2014. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 136(5), 051011 (Jun 12, 2014) (7 pages) Paper No: DS-13-1425; doi: 10.1115/1.4027171 History: Received November 03, 2013; Revised March 03, 2014

The stability boundaries of LTI time-delayed systems with respect to the delays are studied in two different domains: (i) delay space (DS) and (ii) spectral delay space (SDS), which contains pointwise frequency information as well as the delay. SDS is the preferred domain due to its advantageous boundedness properties and simple construct of stability transition boundaries. These transitions at the mentioned boundaries, however, present some conceptual challenges in SDS. This transition property enables us to extract the corresponding local stability variation properties in the DS, while it does not have any implication in the preferred SDS. The novel aspect of the investigation is to introduce a comparison mechanism between these two domains, DS and SDS, from the stability transition perspective. Interestingly, we are able to prove their equivalency, which provides complementary insight to the parametric stability variations.

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Copyright © 2014 by ASME
Topics: Stability , Delays
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Figures

Grahic Jump Location
Fig. 1

SDS for example case study

Grahic Jump Location
Fig. 2

(τ1,τ2) DS for the example case study

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