### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics

### 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

**Semi-discretization.** / Insperger, T.; Stépán, G.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Semi-discretization

AU - Insperger, T.

AU - Stépán, G.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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].

AB - 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].

UR - http://www.scopus.com/inward/record.url?scp=84893683191&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893683191&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-0335-7_3

DO - 10.1007/978-1-4614-0335-7_3

M3 - Chapter

AN - SCOPUS:84893683191

T3 - Applied Mathematical Sciences (Switzerland)

SP - 39

EP - 71

BT - Applied Mathematical Sciences (Switzerland)

PB - Springer

ER -