Constructions of “positive real functions”
نویسندگان
چکیده
منابع مشابه
Properties of Positive Real Functions
The purpose of this note is to develop facts about positive real transfer functions for discretetime linear systems, i.e., in the z plane. Positive real functions arise naturally as the impedance functions of passive continuous-time systems.
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In this paper, we define new subclass of analytic functions related with bounded positive real part, and coefficients estimates, duality and neighborhood are considered.
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A standard result of linear-system theory states that a SISO rational th-order transfer function always has an th-order realization. In some applications, one is interested in having a realization with nonnegative entries (i.e., a positive system) and it is known that a positive system may not be minimal in the usual sense. In this paper, we give an explicit necessary and sufficient condition f...
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In this paper, the class of harmonic functions f = h+ ḡ with positive real part and normalized by f(ζ) = 1, (|ζ| < 1) is studied, where h and g are analytic in U = {z : |z| < 1}. Some properties of this class are searched. Sharp coefficient relations are given for functions in this class. On the other hand, the author make use of Alexander integral transforms of certain analytic functions (whic...
متن کاملReal and complex variable positive definite functions
In this paper we present an overview of the implications of our previously derived results for positive definite kernels on the general theory of positive definite functions. We begin by exploring the consequences of a set of differential inequalities on the global behaviour of a smooth positive definite function of one real variable. Then we propose a natural extension of this study to the com...
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ژورنال
عنوان ژورنال: Applications of Mathematics
سال: 1956
ISSN: 0862-7940,1572-9109
DOI: 10.21136/am.1956.102529