Improvements on the Cluster Treatment of Characteristic Roots and the Case Studies
A recent methodology, the Direct Method (DM), is considered for the stability analysis of the linear time-invariant time-delayed systems (LTI-TDS). Its fundamental strength is in the paradigm called the “cluster treatment of th e characteristic roots” (CTCR). Salient features of the CTCR and the steps of DM are described. An interesting extension to DM is its equally effective utilization for both the retarded and neutral TDS. A well studied necessary condition for NTDS is shown to be an inherent property imbedded within the steps of the DM. Example case studies are given to show the effectiveness of the procedure.
KeywordsTarget Tracking Characteristic Root Cluster Treatment Active Vibration Imaginary Root
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