### Abstract

This paper proposes a closed form solution to L_{2}-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the 2-nd order case of state-space digital filters, we can formulate L _{2}-sensitivity minimization problem by hyperbolic functions. As a result, L_{2}-sensitivity minimization problem can be converted into a problem to find the solution to a 4-th degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations.

Original language | English |
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Title of host publication | ISCAS 2006 |

Subtitle of host publication | 2006 IEEE International Symposium on Circuits and Systems, Proceedings |

Pages | 5223-5226 |

Number of pages | 4 |

Publication status | Published - 2006 Dec 1 |

Event | ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems - Kos, Greece Duration: 2006 May 21 → 2006 May 24 |

### Other

Other | ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems |
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Country | Greece |

City | Kos |

Period | 06/5/21 → 06/5/24 |

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Electrical and Electronic Engineering

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## Cite this

Yamaki, S., Abe, M., & Kawamata, M. (2006). A closed form solution to L2-sensitivity minimization of second-order state-space digital filters. In

*ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems, Proceedings*(pp. 5223-5226). [1693810]