### Abstract

Original language | English |
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Pages (from-to) | 381-400 |

Number of pages | 20 |

Journal | BIT Numerical Mathematics |

Volume | 54 |

Issue number | 2 |

DOIs | |

Publication status | Published - 23 Nov 2013 |

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### Cite this

*BIT Numerical Mathematics*,

*54*(2), 381-400. https://doi.org/10.1007/s10543-013-0457-x

**A new approach for calculating the real stability radius.** / Freitag, M A; Spence, A.

Research output: Contribution to journal › Article

*BIT Numerical Mathematics*, vol. 54, no. 2, pp. 381-400. https://doi.org/10.1007/s10543-013-0457-x

}

TY - JOUR

T1 - A new approach for calculating the real stability radius

AU - Freitag, M A

AU - Spence, A

PY - 2013/11/23

Y1 - 2013/11/23

N2 - We present a new fast algorithm to compute the real stability radius with respect to the open left half plane which is an important problem in many engineering applications. The method is based on a well-known formula for the real stability radius and the correspondence of singular values of a transfer function to pure imaginary eigenvalues of a three-parameter Hamiltonian matrix eigenvalue problem. We then apply the implicit determinant method, used previously by the authors to compute the complex stability radius, to find the critical point corresponding to the desired singular value. This corresponds to a two-dimensional Jordan block for a pure imaginary eigenvalue in the parameter dependent Hamiltonian matrix. Numerical results showing quadratic convergence of the algorithm are given.

AB - We present a new fast algorithm to compute the real stability radius with respect to the open left half plane which is an important problem in many engineering applications. The method is based on a well-known formula for the real stability radius and the correspondence of singular values of a transfer function to pure imaginary eigenvalues of a three-parameter Hamiltonian matrix eigenvalue problem. We then apply the implicit determinant method, used previously by the authors to compute the complex stability radius, to find the critical point corresponding to the desired singular value. This corresponds to a two-dimensional Jordan block for a pure imaginary eigenvalue in the parameter dependent Hamiltonian matrix. Numerical results showing quadratic convergence of the algorithm are given.

UR - http://www.scopus.com/inward/record.url?scp=84887932588&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/s10543-013-0457-x

U2 - 10.1007/s10543-013-0457-x

DO - 10.1007/s10543-013-0457-x

M3 - Article

VL - 54

SP - 381

EP - 400

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

SN - 0006-3835

IS - 2

ER -