On Stability of Parametrized Families of Polynomials and Matrices

Handan Akyar, Taner Büyükköroğlu and Vakıf Dzhafarov

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: The Schur and Hurwitz stability problems for a parametric polynomial family as well as the Schur stability problem for a compact set of real matrix family are considered. It is established that the Schur stability of a family of real matrices 𝒜 is equivalent to the nonsingularity of the family {A2 − 2tA + I : A ∈ 𝒜, t ∈ [−1, 1]} if 𝒜 has at least one stable member. Based on the Bernstein expansion of a multivariable polynomial and extremal properties of a multilinear function, fast algorithms are suggested.

Date: 2010
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https://doi.org/10.1155/2010/687951

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:687951

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