On Stability of Parametrized Families of Polynomials and Matrices

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AKYAR H., BÜYÜKKÖROĞLU T., Dzhafarov V.

ABSTRACT AND APPLIED ANALYSIS, cilt.2010, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2010
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1155/2010/687951
  • Dergi Adı: ABSTRACT AND APPLIED ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anadolu Üniversitesi Adresli: Evet

Özet

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) - 2tA + I : A is an element of A,t is an element of [-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.