On Stability of Parametrized Families of Polynomials and Matrices
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.
Kaynak
Abstract and Applied AnalysisKoleksiyonlar
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