On Stability of Parametrized Families of Polynomials and Matrices

Handan Akyar, Taner Büyükköroğlu and Vakıf Dzhafarov

Abstract and Applied Analysis, 2010, vol. 2010, 1-16

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 ð ’œ is equivalent to the nonsingularity of the family { ð ´ 2 − 2 ð ‘¡ ð ´ + ð ¼ âˆ¶ ð ´ âˆˆ ð ’œ , ð ‘¡ ∈ [ − 1 , 1 ] } if ð ’œ 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:687951

DOI: 10.1155/2010/687951

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