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.
Investigation of Local Stability Transitions in the Spectral Delay Space and Delay Space
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.
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Gao, Q., Zalluhoglu, U., and Olgac, N. (June 12, 2014). "Investigation of Local Stability Transitions in the Spectral Delay Space and Delay Space." ASME. J. Dyn. Sys., Meas., Control. September 2014; 136(5): 051011. https://doi.org/10.1115/1.4027171
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