Abstract
A general class of linear time invariant (LTI) multiple time-delay system is investigated in order to (i) obtain exact lower and upper bounds of crossing frequency set (CFS), and (ii) test the necessary and sufficient conditions of delay independent stability (DIS). The method commences by deploying Rekasius substitution for the transcendental terms in the characteristic function, reducing it into a finite dimensional one. After substitution, utilization of elimination theory allows one to achieve the two nontrivial objectives (i)-(ii). The approach is new and novel as it does not require any parameter sweeping and graphical display; it is exact and can test necessary and sufficient conditions of DIS over only a single variable polynomial. A case study is provided to show the effectiveness of the proposed method.
Keywords
time delay systems, crossing frequency set, stability independent of delay test, stability, multiple time delays, rekasius substitution
Publisher
IFAC
Publication Date
1-1-2009
Rights Information
Copyright © IFAC 2009
Rights Holder
IFAC
Recommended Citation
Delice, Ismail Ilker and Sipahi, Rifat, "Exact upper and lower bounds of crossing frequency set and delay independent stability test for multiple time delayed systems" (2009). Mechanical and Industrial Engineering Faculty Publications. Paper 46.
Notes
Paper presented at the 8th IFAC Workshop on Time-Delay Systems (Romania, 2009). DOI:10.3182/20090901-3-RO-4009.00015