Wronskian-based tests for stability of polynomial combinations
نویسندگان
چکیده
In this paper, a stability criterion based on counting the real roots of two specific polynomials is formulated. To establish this result, it is shown that a hyperbolicity condition and a strict positivity of a polynomial Wronskian are necessary and sufficient for the stability of any real polynomial. This result is extended to the stability study of some linear combinations of polynomials. Necessary and sufficient conditions of stability are obtained for polynomial segments and planes.
منابع مشابه
On the Wronskian Combinants of Binary Forms
For generic binary forms A1, . . . , Ar of order d we construct a class of combinants C = {Cq : 0 ≤ q ≤ r, q 6= 1}, to be called the Wronskian combinants of the Ai. We show that the collection C gives a projective imbedding of the Grassmannian G(r, Sd), and as a corollary, any other combinant admits a formula as an iterated transvectant in the C. Our second main result characterizes those colle...
متن کاملA ug 2 00 3 SELF - SELF - DUAL SPACES OF POLYNOMIALS
A space of polynomials V of dimension 7 is called self-dual if the divided Wronskian of any 6-subspace is in V . A self-dual space V has a natural inner product. The divided Wronskian of any isotropic 3-subspace of V is a square of a polynomial. We call V self-self-dual if the square root of the divided Wronskian of any isotropic 3-subspace is again in V . We show that the self-self-dual spaces...
متن کاملRobust Fixed-order Gain-scheduling Autopilot Design using State-space Stability-Preserving Interpolation
In this paper, a robust autopilot is proposed using stable interpolation based on Youla parameterization. The most important condition of stable interpolation between local controllers is the preservation of stability so that each local controller can ensure stability for an open neighborhood around a nominal point. The proposed design used fixed-order robust controller with parameter-dependent...
متن کاملStability of Recombinant Proteins in Escherichia coli: The Effect of Co-Expression of Five Different Chaperone Sets
Chaperones are produced by prokaryotic, yeast and higher eukaryotic cells for various purposes. Over-expression of each chaperone or sets of them affect the production level of a recombinant protein in the cell. On the basis of this hypothesis, five different plasmids with 5 different combinations of 6 chaperones molecule, transformed into Escherichia coli along with human basic Fibroblast Grow...
متن کاملJeu de taquin and a monodromy problem for Wronskians of polynomials
The Wronskian associates to d linearly independent polynomials of degree at most n, a non-zero polynomial of degree at most d(n−d). This can be viewed as giving a flat, finite morphism from the Grassmannian Gr(d, n) to projective space of the same dimension. In this paper, we study the monodromy groupoid of this map. When the roots of the Wronskian are real, we show that the monodromy is combin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Systems & Control Letters
دوره 60 شماره
صفحات -
تاریخ انتشار 2011