In this note, the analysis of time delay systems (TDSs) using Lambert W function approach is reassessed. A common canonical (CC) form of time delay systems is defined. We extended the recent results of Cepeda–Gomez and Michiels (2015, “Some Special Cases in the Stability Analysis of Multi-Dimensional Time-Delay Systems Using the Matrix Lambert W Function,” Automatica, 53, pp. 339–345) for second-order into nth order system. The eigenvalues of a time delay system are either real or complex conjugate pairs and therefore, the whole eigenspectrum can be associated with only two real branches of the Lambert W function. A new class of time delay systems is characterized to extend the applicability of the above-said method. Moreover, this approach has been exploited to design a controller which places a subset of eigenvalues at desired locations. Stability is guaranteed by using a new algorithm developed in this paper, which is based on the Nyquist plot. The approach is validated through numerical examples.
Analysis of Multidimensional Time Delay Systems Using Lambert W Function
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 11, 2016; final manuscript received May 10, 2017; published online August 8, 2017. Assoc. Editor: Davide Spinello.
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Choudhary, N., Sivaramakrishnan, J., and Narayan Kar, I. (August 8, 2017). "Analysis of Multidimensional Time Delay Systems Using Lambert W Function." ASME. J. Dyn. Sys., Meas., Control. November 2017; 139(11): 114506. https://doi.org/10.1115/1.4036874
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