On Stability of Parametrized Families of Polynomials and Matrices
Handan Akyar, Taner Büyükköroğlu, Vakıf Dzhafarov · Abstract and Applied Analysis · 2010
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 matrices𝒜is equivalent to the nonsingularity of the family {A2− 2tA+I:A∈𝒜,t∈ [−1, 1]} if𝒜has 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.