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Operations Research, Systems Engineering and Industrial Engineering

Cluster treatment of characteristic roots (CTCR)

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Full-Text Articles in Mechanical Engineering

Complete Stability Map Of First Order - Two Time Delay Systems With Delay Cross-Talk, Rifat Sipahi, Nejat Olgac Apr 2012

Complete Stability Map Of First Order - Two Time Delay Systems With Delay Cross-Talk, Rifat Sipahi, Nejat Olgac

Rifat Sipahi

First order linear time invariant dynamics is taken into account with two delays. A unique feature is included in this study, from the stability perspective: a term that represents the cross-talk between the two delays. This class of systems can be treated by a unique procedure, which is recently developed, known as Cluster Treatment of Characteristic Roots (CTCR). In the text we present several case studies to display the steps and the strengths of CTCR. We also include some comparison results with respect to a cornerstone study (Hale, and Huang, 1993), which gives a wonderful point of reference for this ...


Complete Stability Analysis Of Neutral‐Type First Order Two‐Time‐Delay Systems With Cross‐Talking Delays, Rifat Sipahi, Nejat Olgac Apr 2012

Complete Stability Analysis Of Neutral‐Type First Order Two‐Time‐Delay Systems With Cross‐Talking Delays, Rifat Sipahi, Nejat Olgac

Rifat Sipahi

The stability robustness of first order linear time invariant dynamics of neutral type with multiple time delays against delay uncertainties is taken into consideration. We depart from a simpler investigation of Hale and Huang [J. Math. Anal. Appl., 178 (1993), pp. 344–362], which studies the same problem for retarded‐type systems. On this basis we further introduce two challenging features by including (a) terms that add neutral dynamics and (b) an additional term that introduces cross‐talk between the multiple delays. To the best of the authors’ knowledge, the stability posture of this class of systems can be treated ...