BIT Numerical Mathematics

, Volume 54, Issue 2, pp 381–400 | Cite as

A new approach for calculating the real stability radius

  • Melina A. Freitag
  • Alastair Spence


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.


Real stability radius Numerical methods Structured perturbations 

Mathematics Subject Classification (2010)

65F15 58C15 93B60 



The authors would like to thank Prof Paul Van Dooren (Université Catholique de Louvain) for helpful discussions and pointing us to some relevant literature. Moreover we would like to thank the anonymous referees and the associate editor for their comments which helped to improve the paper.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of BathBathUK

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