Minimal McMillan degree rational matrix functions with prescribed local zero-pole structure
نویسندگان
چکیده
منابع مشابه
On minimal degree simultaneous pole assignment problems
In this paper, we show that a generic r-tuple of m-input p-output linear systems is simultaneously pole assignable if r < m+ p and the McMillan degrees of the systems are not too different. We also obtain upper bounds for the degrees of the compensators which simultaneously assign the characteristic polynomials of the r-tuple of closed loop systems. The upper bounds are obtained for each of the...
متن کاملPlane Curves of Minimal Degree with Prescribed Singularities
We prove that there exists a positive α such that for any integer d ≥ 3 and any topological types S1, . . . , Sn of plane curve singularities, satisfying μ(S1) + · · ·+ μ(Sn) ≤ αd, there exists a reduced irreducible plane curve of degree d with exactly n singular points of types S1, . . . , Sn, respectively. This estimate is optimal with respect to the exponent of d. In particular, we prove tha...
متن کاملMinimal degree univariate piecewise polynomials with prescribed Sobolev regularity
For k ∈ {1, 2, 3, . . . }, we construct an even compactly supported piecewise polynomial ψk whose Fourier transform satisfies Ak(1 + ω ) ≤ b ψk(ω) ≤ Bk(1 + ω ), ω ∈ R, for some constants Bk ≥ Ak > 0. The degree of ψk is shown to be minimal, and is strictly less than that of Wendland’s function φ1,k−1 when k > 2. This shows that, for k > 2, Wendland’s piecewise polynomial φ1,k−1 is not of minima...
متن کاملOn the Pole and Zero Locations of Rational Laplace Transformations of Non-negative Functions
1. L. Fejer, Neue Eigenschaften der Mittelwerte bei den Fourierreihen, J. London Math. Soc. vol. 8 (1933) pp. 53-62. 2. M. S. Robertson, On the coefficients of a typically-real function, Bull. Amer. Math. Soc. vol. 41 (1935) pp. 565-572. 3. W. Rogosinski, Uber positive harmonische Enlwicklungen und typischreelle Potenzreihen, Math. Z. vol. 35 (1932) pp. 93-121. 4. W. T. Scott and H. S. Wall, Th...
متن کاملWeighted Turán Type Inequality for Rational Functions with Prescribed Poles
Firstly, we introduce a new type of weight functions named as N-doubling weights, which is an essential generalization of the well known doubling weights. Secondly, we establish a weighted Turán type inequality with N-doubling weights and a Nikolskii-Turán type inequality for rational functions with prescribed poles. Our results generalize some known Turán type inequality both for polynomials a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1990
ISSN: 0024-3795
DOI: 10.1016/0024-3795(90)90133-w