A least-square spectral element method for stability analysis of time delay systems∗

This paper presents a numerical method for the stability analysis of retarded functional differential equations with time-periodic coeficients. The method approximates the solution segments, corresponding to the end points of the principal period, by their piecewise Lagrange interpolants. Then a mapping between these solution segments is obtained by the minimization of the least-square integral of the residual error. Finally, stability properties are determined using the matrix approximation of the monodromy operator, obtained by this mapping, according to the Floquet theorem. The formulation of the method is presented for an equation of general type while results are shown for the delayed oscillator.