Analysis of Multidimensional Time Delay Systems Using Lambert W Function

作者：Choudhary Niraj; Sivaramakrishnan Janardhanan; Kar Indra Narayan

来源：Journal of Dynamic Systems Measurement and Control-Transactions of the ASME, 2017, 139(11): 114506.

DOI：10.1115/1.4036874

<jats:p>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.</jats:p>

• 出版日期2017-11
• 单位Indian Institute of Technology