### 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].

Original language | English |
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Title of host publication | Applied Mathematical Sciences (Switzerland) |

Publisher | Springer |

Pages | 39-71 |

Number of pages | 33 |

DOIs | |

Publication status | Published - Jan 1 2011 |

### Publication series

Name | Applied Mathematical Sciences (Switzerland) |
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Volume | 178 |

ISSN (Print) | 0066-5452 |

ISSN (Electronic) | 2196-968X |

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

*Applied Mathematical Sciences (Switzerland)*(pp. 39-71). (Applied Mathematical Sciences (Switzerland); Vol. 178). Springer. https://doi.org/10.1007/978-1-4614-0335-7_3