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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Semi-discretization
verfasst von : Tamás Insperger, Gábor Stépán
Erschienen in: Semi-Discretization for Time-Delay Systems
Verlag: Springer New York
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Stability analysis of DDEs with time-periodic coefficients requires the analysis of the eigenvalues of the infinite-dimensional monodromy operator. Generally, stability conditions cannot be given as closed-form functions of the system parameters (the delayed Mathieu equation in Section 2.4 is an exception), but numerical approximations can be used to derive stability properties. Semi-discretization is an efficient numerical method that provides a finite-dimensional matrix approximation of the infinite-dimensional monodromy matrix. This chapter presents the main concept of the semi-discretization method for general linear time-periodic DDEs following [123, 73, 126, 101, 133].