### Abstract

In transient analysis of electrical circuits the solution is computed by
means of numerical integration methods. Adaptive stepsize control is used to control
the local errors of the numerical solution. For optimization purposes smoother
stepsize controllers can ensure that the errors and stepsizes also behave smoothly.
For onestep methods, the stepsize control process can be viewed as a digital (i.e.
discrete) linear control system for the logarithms of the errors and steps. For the
multistep BDF-method this control process can be approximated by such a linear
control system.

Original language | English |
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Title of host publication | Scientific Computing in Electrical Engineering (Proceedings SCEE-2004, Capo D'Orlando, Sicily, Italy, September 5-9, 2004) |

Editors | A.M. Anile, G. Ali, G. Mascali |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 137-142 |

ISBN (Print) | 3-540-32861-0 |

Publication status | Published - 2006 |

### Publication series

Name | Mathematics in Industry |
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Volume | 9 |

ISSN (Print) | 1612-3956 |

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## Cite this

Verhoeven, A., Beelen, T. G. J., Hautus, M. L. J., & Maten, ter, E. J. W. (2006). Digital linear control theory for automatic stepsize control. In A. M. Anile, G. Ali, & G. Mascali (Eds.),

*Scientific Computing in Electrical Engineering (Proceedings SCEE-2004, Capo D'Orlando, Sicily, Italy, September 5-9, 2004)*(pp. 137-142). (Mathematics in Industry; Vol. 9). Springer.