Optimization of functionals of Hurwitz polynomials
نویسندگان
چکیده
منابع مشابه
On Robust Hurwitz Polynomials
In this note, Kharitonov's theorem on robust Hunvitz poljmomials is simplified for low-order polynomials. Specifically, for n = 3, 4, and 5, the number of polynomials required to check robust stability is one, two, and three, respectively, instead of four. Furthermore, it is shown that for n > 6, the number of polynomials for robust stability checking is necessarily four, thus further simplific...
متن کاملHadamard Factorization of Hurwitz Stable Polynomials
The Hurwitz stable polynomials are important in the study of differential equations systems and control theory (see [7] and [19]). A property of these polynomials is related to Hadamard product. Consider two polynomials p, q ∈ R[x]: p(x) = anx n + an−1x n−1 + · · ·+ a1x + a0 q(x) = bmx m + bm−1x m−1 + · · ·+ b1x + b0 the Hadamard product (p ∗ q) is defined as (p ∗ q)(x) = akbkx + ak−1bk−1x + · ...
متن کاملLocal convex directions for Hurwitz stable polynomials
A new condition for a polynomial ( ) to be a local convex direction for a Hurwitz stable polynomial ( ) is derived. The condition is in terms of polynomials associated with the even and odd parts of ( ) and ( ), and constitutes a generalization of Rantzer’s phase-growth condition for global convex directions. It is used to determine convex directions for certain subsets of Hurwitz stable polyno...
متن کاملRobust Hurwitz stability of polytopes of complex polynomials
The main goal of this note is to provide a complete tool for verifying whether polytopes of complex polynomials whose degrees differ at most by one are Hurwitz stable. The results extend some classical theorems, such as the Edge Theorem given by Bartlett, Hollot and Huang (1988), its generalizations proposed by Sideris and Barmish (1989), Fu and Barmish (1989), and the eigenvalue criterion give...
متن کاملAlmost strict total positivity and a class of Hurwitz polynomials
We establish sufficient conditions for a matrix to be almost totally positive, thus extending a result of Craven and Csordas who proved that the corresponding conditions guarantee that a matrix is strictly totally positive. Then we apply our main result in order to obtain a new criteria for a real algebraic polynomial to be a Hurwitz one. The properties of the corresponding “extremal” Hurwitz p...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1989
ISSN: 0024-3795
DOI: 10.1016/0024-3795(89)90386-8