On Stability of Parametrized Families of Polynomials and Matrices - Handan Akyar; Taner Büyükköroğlu; Vakıf Dzhafarov (Abstract and Applied Analysis)
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 {𝐴2−2𝑡𝐴+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.