# On multiple-delay approximations of multiple-derivative controllers

Wan, Yan
and
Roy, Sandip
and
Stoorvogel, Anton
and
Saberi, Ali
(2009)
*On multiple-delay approximations of multiple-derivative controllers.*
In: European Control Conference, ECC 2009, 23-26 August 2009, Budapest, Hungary (pp. pp. 4163-4168).

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Abstract: | We study approximation of multiple-derivative output feedback for linear time-invariant (LTI) plants using multiple-delay approximations. We obtain a condition on the plant and feedback that yields an equivalence between the closed-loop spectra for the approximate feedbacks and the desired multiple-derivative feedbacks. On the other hand, we use a scalar example to illustrate that multiple-delay approximations of sufficiently high derivatives may in some cases yield closed-loop spectra that differ greatly from the dynamics upon derivative feedback (for instance, containing many and very large right half plane poles), while in other cases replicating the derivative feedback perfectly. Finally, through understanding this dichotomy, we present a condition for stabilizing a SISO relative degree-1 plant when a delay implementation of the first-order derivative is used in the output feedback control law. |

Item Type: | Conference or Workshop Item |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/67843 |

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