Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL
ACM Transactions on Mathematical Software (TOMS)
On Stability of LMS Methods and Characteristic Roots of Delay Differential Equations
SIAM Journal on Numerical Analysis
Stability of Time-Delay Systems
Stability of Time-Delay Systems
Pseudospectral Differencing Methods for Characteristic Roots of Delay Differential Equations
SIAM Journal on Scientific Computing
Efficient computation of characteristic roots of delay differential equations using LMS methods
Journal of Computational and Applied Mathematics
Stability and Stabilization of Time-Delay Systems (Advances in Design & Control) (Advances in Design and Control)
Solution operator approximations for characteristic roots of delay differential equations
Applied Numerical Mathematics
Automatica (Journal of IFAC)
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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.