A new approach for calculating the real stability radius

M A Freitag, A Spence

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)381-400
Number of pages20
JournalBIT Numerical Mathematics
Volume54
Issue number2
DOIs
Publication statusPublished - 23 Nov 2013

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Stability Radius
Hamiltonian Matrix
Hamiltonians
Singular Values
Jordan Block
Eigenvalue
Quadratic Convergence
Engineering Application
Half-plane
Transfer Function
Fast Algorithm
Eigenvalue Problem
Transfer functions
Critical point
Determinant
Correspondence
Numerical Results
Dependent

Cite this

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

In: BIT Numerical Mathematics, Vol. 54, No. 2, 23.11.2013, p. 381-400.

Research output: Contribution to journalArticle

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