On Stability of Parametrized Families of Polynomials and Matrices

الملخص EN

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.