Abstract
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].
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© 2011 Springer Science+Business Media, LLC
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Insperger, T., Stépán, G. (2011). Semi-discretization. In: Semi-Discretization for Time-Delay Systems. Applied Mathematical Sciences, vol 178. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0335-7_3
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DOI: https://doi.org/10.1007/978-1-4614-0335-7_3
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-0334-0
Online ISBN: 978-1-4614-0335-7
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