In this work we address the question of asymptotic stability of linear delay differential equations (DDEs) with time periodic coefficients, a class which is recognized to be fundamental in machining tool. Since the dynamics of such a class of delay systems is governed by the dominant eigenvalues (multipliers) of the monodromy operator associated to the system of DDEs, i.e. the solution operator over the period of the coefficients, we discretize it by using pseudospectral differencing techniques based on collocation and approximate the dominant multipliers by the eigenvalues of the resulting matrix. The use of pseudospectral methods has already been proposed in the context of simpler DDEs. Here we fully generalize the method to the class of linear time periodic coefficients DDEs with arbitrary period and multiple discrete and distributed delays. The scheme is shown to have spectral accuracy by means of several numerical examples.

Numerical computation of characteristic multipliers for linear time periodic coefficients delay differential equations

BREDA, Dimitri;VERMIGLIO, Rossana
2006-01-01

Abstract

In this work we address the question of asymptotic stability of linear delay differential equations (DDEs) with time periodic coefficients, a class which is recognized to be fundamental in machining tool. Since the dynamics of such a class of delay systems is governed by the dominant eigenvalues (multipliers) of the monodromy operator associated to the system of DDEs, i.e. the solution operator over the period of the coefficients, we discretize it by using pseudospectral differencing techniques based on collocation and approximate the dominant multipliers by the eigenvalues of the resulting matrix. The use of pseudospectral methods has already been proposed in the context of simpler DDEs. Here we fully generalize the method to the class of linear time periodic coefficients DDEs with arbitrary period and multiple discrete and distributed delays. The scheme is shown to have spectral accuracy by means of several numerical examples.
2006
9783902661111
File in questo prodotto:
File Dimensione Formato  
2006_ifac_breda_maset_vermiglio.pdf

non disponibili

Tipologia: Documento in Post-print
Licenza: Non pubblico
Dimensione 214.14 kB
Formato Adobe PDF
214.14 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/847700
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? ND
social impact