Reliably computing all characteristic roots of delay differential equations in a given right half plane using a spectral method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Wu, Zhen¹  Michiels, Wim¹ 

[1] Katholieke Univ Leuven, Dept Comp Sci, B-3001 Heverlee, Belgium

关键词: Delay differential equations;    Characteristic root;    Spectral discretization;    Rational approximation;   

DOI  :  10.1016/j.cam.2011.12.009

来源: Elsevier

【 摘 要 】

Spectral discretization methods are well established methods for the computation of characteristic roots of time-delay systems. In this paper a method is presented for computing all characteristic roots in a given right half plane. In particular, a procedure for the automatic selection of the number of discretization points is described. This procedure is grounded in the connection between a spectral discretization and a rational approximation of exponential functions. First, a region that contains all desired characteristic roots is estimated. Second, the number of discretization points is selected in such a way that in this region the rational approximation of the exponential functions is accurate. Finally, the characteristic roots approximations, obtained from solving the discretized eigenvalue problem, are corrected up to the desired precision by a local method. The effectiveness and robustness of the procedure are illustrated with several examples and compared with DDE-BIFTOOL. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free