On Stability of Parametrized Families of Polynomials and Matrices
ABSTRACT AND APPLIED ANALYSIS, cilt.2010, 2010 (SCI-Expanded, Scopus)
- 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
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- 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.