Abstract and Applied Analysis

On Stability of Parametrized Families of Polynomials and Matrices

Handan Akyar, Taner Büyükköroğlu, and Vakıf Dzhafarov

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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 { A 2 2 t A + 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.

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Abstr. Appl. Anal., Volume 2010 (2010), Article ID 687951, 16 pages.

First available in Project Euclid: 1 November 2010

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Akyar, Handan; Büyükköroğlu, Taner; Dzhafarov, Vakıf. On Stability of Parametrized Families of Polynomials and Matrices. Abstr. Appl. Anal. 2010 (2010), Article ID 687951, 16 pages. doi:10.1155/2010/687951. https://projecteuclid.org/euclid.aaa/1288620782

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