Necessary conditions 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...
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This paper concerns the Schur stability of polynomials. Firstly necessary conditions are presented for the Schur stability of complex polynomials with fixed coefficients based on the discrete Hermite-Biehler theorem. Then the result is applied to obtain necessary conditions for the robust Schur stability of real interval polynomials.
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 + · ...
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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 کاملOn the Necessary and Sufficient Conditions for the Very Strict Hurwitz Property
Necessary and sufficient conditions for the bi-variate characteristic polynomial of a matrix to be very strict Hurwitz (VSHP) are presented. These conditions are based on solving the Lyapunov equation for 2 0 continuous systems using the Kronecker product and lead to a simple test for the VSHP property. It requires testing only the eigenvalues of three stable matrices and this is simpler than t...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(02)00432-9