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37th Chinese Control Conference (CCC)

作者： Xue, Weimin Teng, Yanmei Wang, Lei Chen, Michael Z. Q. Wang, Qing-guo Beihang Univ Sch Math & Syst Sci Beijing 100191 Peoples R China Beihang Univ Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Jiangsu Peoples R China Univ Johannesburg Fac Engn & Built Environm Inst Intelligent Syst Johannesburg South Africa

ISBN: (纸本)9789881563958

This paper deals with the realizability of a bicubic impedance function with one resistive element and three reactive elements. It would be too complex to determine the positive realness of the impedance function if we enumerate all the possible networks. To solve this problem, we assume that a bicubic impedance function is obtained by a class of networks described by a circuit with a biquadratic impedance function in series or parallel with another circuit of a single reactive element. Then, we show the positive real relationship between them, and provide all the realizations of the bicubic impedance function by one resistive element and three reactive elements. Finally, two examples are given for illustration and validation of our results.

关键词： realization Bicubic Impedance Biquadratic Impedance Reactive Elements positive real function

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All discrete-time positive real functions interpolating input-output characteristics

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2000年第3期E83A卷 507-515页

作者： Horiguchi, K Kinki Univ Fac Biol Oriented Sci & Technol Wakayama 6496493 Japan

It is an important problem in signal processing, system realization and system identification to find linear discrete-time systems which are consistent with given covariance parameters. This problem is formulated as a problem of finding discrete-time positive real functions which interpolate given covariance parameters. Among Various solutions to the problem, a recent remarkable one is a parameterization of all the discrete-time strictly positive real functions that interpolate the covariance parameters and have a limited McMillan degree. In this paper, we use more general input-output characteristics than covariance parameters and consider finding discrete-time positive real functions which interpolate such characteristics. The input-output characteristics are given by the coefficients of the Taylor series at some complex points in the open unit disk. Based on our previous work, we present an algorithm to generate all the discrete-time positive real functions that interpolate the input-output characteristics and have a limited McMillan degree. The algorithm is more general and simpler than the previous one, and is an important practical supplement to the previous work. Moreover, the interpolation of the general input-output characteristics can be effectively applied to the frequency-weighted model reduction. Hence, the algorithm makes a contribution to the problem from the practical viewpoint as well as the theoretical viewpoint.

关键词： positive real function interpolation input-output characteristics realization theory

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Caratheodory-Toeplitz based mathematical methods and their algorithmic applications in biometric image processing

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APPLIED NUMERICAL MATHEMATICS 2014年 75卷 2-21页

作者： Saeed, Khalid AGH Univ Sci & Technol Fac Phys & Appl Comp Sci PL-30059 Krakow Poland

In this paper the application of bounded series theory due to Caratheodory and Toeplitz is explored to study Brune positive real rational function (PRF). The main goal is to find the necessary and sufficient conditions for PRF coefficients. The introduced algorithms and assertions present an appropriate mathematical model derived from the developed analytical functions. The suggested solution is based on the results of Caratheodory, Toeplitz, Schur and their achievements at the beginning of the twentieth century. Toeplitz matrix lowest eigenvalues are constructed by the coefficients of the bounded power series representing Caratheodory function to establish a new simple and general algorithm for testing the nonnegativeness of real rational functions. The achieved results have shown engineering interests in two different areas of research: the electrical and mechanical circuit theory from one side and the image analysis and processing from the other side. The involvement in these methods has recently drawn the attention of researchers due to the increasing demand for simple methods of electrical and mechanical network synthesis. The author has proved the reasonability of Caratheodory-Toeplitz theory and modified it for using in other new areas of research. The most important achievements that describe relevant applications in such fields as digital filter design, speech signal and object image processing are discussed in the paper. Examples are introduced to illustrate these applications with emphasis on biometrics. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Caratheodory-Toeplitz theory Circuit theory Digital filter realization Image description for object recognition positive real function Cognitive informatics Signal and image processing Toeplitz matrix minimal eigenvalues

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Krylov-subspace methods for reduced-order modeling in circuit simulation

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2000年第1-2期123卷 395-421页

作者： Freund, RW Bell Labs Lucent Technol Murray Hill NJ 07974 USA

The simulation of electronic circuits involves the numerical solution of very large-scale, sparse, in general nonlinear, systems of differential-algebraic equations. Often, the size of these systems can be reduced considerably by replacing the equations corresponding to linear subcircuits by approximate models of much smaller state-space dimension. In this paper, we describe the use of Krylov-subspace methods for generating such reduced-order models of linear subcircuits. Particular emphasis is on reduced-order modeling techniques that preserve the passivity of linear RLC subcircuits. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： Lanczos algorithm Arnoldi process linear dynamical system VLSI interconnect transfer function Pade approximation stability passivity positive real function

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Sharp Inequalities for Driving Point Impedance functions

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2023年第9期70卷 3273-3277页

作者： Azeroglu, Tahir Aliyev Ornek, Bulent Nafi Duzenli, Timur Istanbul Arel Univ Dept Comp Engn TR-34537 Istanbul Turkiye Amasya Univ Dept Comp Engn TR-05100 Amasya Turkiye Amasya Univ Dept Elect & Elect Engn TR-05100 Amasya Turkiye

In this brief, positive real functions are considered as driving point impedance functions, Z(s), which are utilized in electrical engineering for characteristic representation of circuits. Accordingly, for the real part of Z(s), sharp inequalities are presented with their extremal functions by using zeros and poles of Z(s). For these extremal functions, corresponding generic circuit schematics are given with their spectral analyses. According to the obtained results, it has been shown that various circuits can be obtained by using the extremal functions of the inequalities presented in this brief.

关键词： Poles and zeros Impedance Capacitors Taylor series Inductors Spectral analysis Signal processing positive real function driving point impedance function extremal function circuit

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Circuit Applications of Schwarz-Pick Lemma

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2022年第1期69卷 20-24页

作者： Duzenli, Timur Amasya Univ Dept Elect & Elect Engn TR-05100 Amasya Turkey

In this brief, the relation between Schwarz-Pick lemma and driving point impedance function is investigated. Schwarz-Pick lemma is given as the generalized version of Schwarz lemma. Here, a generic driving point impedance function is obtained by applying Schwarz-Pick lemma to positive real functions. At first, a novel inequality is obtained for the modulus of the derivative of the driving point impedance function and in the next step, an extremal function is found by applying sharpness analysis to this inequality. At the end, obtained extremal function is considered as a generic driving point impedance function and corresponding circuit schematics are presented with their spectral analyses. Obtained driving point impedance function is not an arbitrary function but it is the intuitive result of the considered problem in this study. Accordingly, it is guaranteed to obtain a practically realizable driving point impedance function. Also, novel upper bounds are determined for the magnitude of driving point impedance function and for its derivative.

关键词： Impedance Circuits and systems Upper bound Resonant frequency RLC circuits Poles and zeros Circuit synthesis Schwarz-Pick lemma positive real function driving point impedance function sharpness analysis extremal function circuit

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Third-Order Hankel Determinant for Transforms of the Reciprocal of Bounded Turning functions

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MATHEMATICAL NOTES 2019年第3-4期105卷 535-542页

作者： Krishna, D. Vamshee RamReddy, T. Shalini, D. GITAM Univ Dept Math Visakhapatnam 530045 Andhra Pradesh India Kakatiya Univ Dept Math Warangal 506009 TS India Dr BR Ambedkar Univ Dept Math Srikakulam 532410 AP India

In this paper, we make an attempt to introduce a new subclass of analytic functions. Using the Toeplitz determinants, we obtain the best possible upper bound for the third-order Hankel determinant associated with the k(th) root transform [f(z(k))](1/k) of the normalized analytic function f(z) when it belongs to this class, defined on the open unit disc in the complex plane.

关键词： analytic function upper bound reciprocal of a bounded turning function third Hankel functional positive real function Toeplitz determinants

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Resolvent representations for functions of sectorial operators

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ADVANCES IN MATHEMATICS 2017年 308卷 896-940页

作者： Batty, Charles Gomilko, Alexander Tomilov, Yuri Univ Oxford St Johns Coll Oxford OX1 3JP England Nicolas Copernicus Univ Fac Math & Comp Sci Ul Chopina 12-18 PL-87100 Torun Poland Natl Acad Sci Ukraine Inst Telecommun & Global Informat Space Kiev Ukraine Polish Acad Sci Inst Math Sniadeckich 8 PL-00956 Warsaw Poland

We obtain integral representations for the resolvent of psi(A), where is a holomorphic function mapping the right half plane and the right half-axis into themselves, and psi is a sectorial operator on a Banach space. As a corollary, for a wide class of functions psi, we show that the operator psi(A) generates a sectorially bounded holomorphic C-0-semigroup on a Banach space whenever -A does, and the sectorial angle of A is preserved. When psi is a Bernstein function, this was recently proved by Gomilko and Tomilov, but the proof here is more direct. Moreover, we prove that such a permanence property for A can be described, at least on Hilbert spaces, in terms of the existence of a bounded H-infinity-calculus for A. As byproducts of our approach, we also obtain new results on functions mapping generators of bounded semigroups into generators of holomorphic semigroups and on subordination for Ritt operators. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Sectorial operator Holomorphic C-0-semigroup Bernstein function positive real function functional calculus Ritt operator Subordination

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COEFFICIENT INEQUALITY FOR CERTAIN SUBCLASSES OF ANALYTIC functionS ASSOCIATED WITH HANKEL DETERMINANT

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INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS 2015年第1期46卷 91-106页

作者： Krishna, D. Vamshee Reddy, T. Ram GITAM Univ GIT Dept Math Visakhapatnam 530045 Andhra Pradesh India Kakatiya Univ Dept Math Warangal 506009 Andhra Pradesh India

The objective of this paper is to obtain an upper bound to the functional vertical bar a(2)a(4) -a(3)(2)vertical bar for the function f and its inverse belonging to certain subclasses of analytic functions, using Toep... 详细信息

关键词： Analytic function lambda-spiral starlike and convex lambda-spiral functions upper bound second Hankel determinant positive real function Toeplitz determinants

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An Upper Bound to the Second Hankel Determinant for functions in Mocanu Class

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VIETNAM JOURNAL OF MATHEMATICS 2015年第3期43卷 541-549页

作者： Deekonda, Vamshee Krishna Thoutreddy, RamReddy GITAM Univ GIT Dept Math Visakhapatnam 530045 Andhra Pradesh India Kakatiya Univ Dept Math Warangal 506009 Andhra Pradesh India

objective of this paper is to obtain an upper bound to the second Hankel determinant vertical bar a(2)a(4) - a(3)(2) vertical bar for the function integral belonging to the Mocanu class, using Toeplitz determinants. T... 详细信息

关键词： Analytic function beta-convex function Starlike and convex functions Upper bound Second Hankel determinant positive real function Toeplitz determinants

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