On Stability of Parametrized Families of Polynomials and Matrices

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AKYAR H., BÜYÜKKÖROĞLU T., Dzhafarov V.

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

  • Publication Type: Article / Article
  • Volume: 2010
  • Publication Date: 2010
  • Doi Number: 10.1155/2010/687951
  • Journal Name: ABSTRACT AND APPLIED ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anadolu University Affiliated: Yes

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 {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.