An EnestrÖm-Kakeya Theorem for Hermitian Polynomial Matrices
نویسندگان
چکیده
We extend the Eneström-Kakeya theorem and its refinement by Hurwitz to polynomial matrices H(z) with positive semidefinite coefficients. We determine an annular region containing the zeros of detH(z). A stability result for systems of linear difference equations is given as an application.
منابع مشابه
Polynomial Matrices with Hermitian Coefficients and a Generalization of the Eneström–kakeya Theorem
Polynomial matrices G(z) = Izm−Cizi with hermitian coefficients Ci are studied. The assumption ∑ |Ci| I implies that the characteristic values of G(z) lie in the closed unit disc. The characteristic values of modulus one are roots of unity. An extension of the Eneström– Kakeya theorem is proved and a stability criterion for a system of difference equations is given. Mathematics subject classifi...
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عنوان ژورنال:
- IEEE Trans. Automat. Contr.
دوره 52 شماره
صفحات -
تاریخ انتشار 2007