Synthesis of two-dimensional losslessm-Ports with prescribed scattering matrix

Kummert, Anton

doi:10.1007/bf01598747

Cited by 67 publications

(36 citation statements)

References 14 publications

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“…Passivity in this sense is to be understood to hold with respect to any of the independent variables, i.e., to hold as if all independent variables were generalizations of time. This is indeed the position adopted in all classical texts on passive MD circuits [Youla 1966;Koga 1968;Rao 1969;Bose 1979;Bose 1982;Bose 1985;Kaczorek 1985;Fettweis 1986b;Fettweis and Basu 1987;Basu and Fettweis 1987;Kummert 1989]. In order to avoid confusion with concepts needed later we will therefore refer to the property just discussed as MD passivity.…”

Section: Multidimensional Wave Digital Filtersmentioning

confidence: 91%

Transformation approach to numerically integrating PDEs by means of WDF principles

Fettweis

Nitsche

1991

Multidim Syst Sign Process

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Abstract. As has been shown, attractive methods for numerically integrating partial differential equations (PDEs) resulting from physical problems can be obtained by simulating the actual physical passive (conservation of energy) dynamical system by means of a discrete passive dynamical system, and this in such a way that the full parallelism and the exclusively local nature of the interconnections (principle of action at proximity) are preserved. An alternative approach for developing such methods is presented which, while still using principles of the same type as those on which multidimensional wave digital filters (WDFs) are based, involves appropriate transformations of the original coordinates of the physical problem at hand. This alternative approach is not only easier to apply than the one referred to above but also more general; it is illustrated on the one hand by the same examples as those that have been used for the other approach, and on the other by showing the applicability to Maxwell's equations.

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Section: Multidimensional Wave Digital Filtersmentioning

confidence: 91%

Transformation approach to numerically integrating PDEs by means of WDF principles

Fettweis

Nitsche

1991

Multidim Syst Sign Process

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“…1 (Multidimensional linear systems whose coefficient matrix has a structure of (1.3), though without any norm constraints on its blocks, and whose transfer function has the form ( 1.4), were introduced in [27,28]; see ( 6.2) for the explicit form of the system equations. ) We also note that the equivalence (1)⇔(3) in Theorem 1.2 for the case of rational inner matrix-valued functions on the bidisk D 2 was independently proved by Kummert [38] in a stronger form: the spaces H 1 , H 2 in (3) are finite-dimensional. This strengthening of Agler's theorem, which also includes item (2) of Theorem 1.2 with rational matrix-valued functions H 1 , …, H d , appears also in [14,26,35].…”

Section: So That S(z) Is Realized In the Formmentioning

confidence: 94%

Scattering Systems with Several Evolutions and Formal Reproducing Kernel Hilbert Spaces

Ball

Kaliuzhnyi-Verbovetskyi

Sadosky³

et al. 2014

Complex Anal. Oper. Theory

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A Schur-class function in d variables is defined to be an analytic contractiveoperator valued function on the unit polydisk. Such a function is said to be in the Schur-Agler class if it is contractive when evaluated on any commutative d-tuple of strict contractions on a Hilbert space. It is known that the Schur-Agler class is a strictly proper subclass of the Schur class if the number of variables d is more than two. The Schur-Agler class is also characterized as those functions arising as the transfer function of a certain type (Givone-Roesser) of conservative multidimensional linear system. Previous work of the authors identified the Schur-Agler class as those Schurclass functions which arise as the scattering matrix for a certain type of (not necessarily minimal) Lax-Phillips multievolution scattering system having some additional geoCommunicated by Irene Sabadini.C. Sadosky passed away in December 2010. We lost a collaborator of many years, and a wonderful friend. Like many others, we miss her. J. A. Ball et al. metric structure. The present paper links this additional geometric scattering structure directly with a known reproducing-kernel characterization of the Schur-Agler class. We use extensively the technique of formal reproducing kernel Hilbert spaces that was previously introduced by the authors and that allows us to manipulate formal power series in several commuting variables and their inverses (e.g., Fourier series of elements of L 2 on a torus) in the same way as one manipulates analytic functions in the usual setting of reproducing kernel Hilbert spaces.

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“…Example 3. We will discuss the passivity of a fractional-order circuit whose impedance function is Z s ð Þ ¼ 0:75s 0:9 þ 0:5s 0:7 þ 2s 0:8 þ 2s 0:6 1:5s 0:4 þ s 0:2 (38) 5 | CONCLUSIONS In this paper, by aid of generalized Tellegen's theorem and multivariable PR theory, we propose new passivity criteria for linear fractional networks in consideration of the invalidity of the existing PR criteria for fractional networks. Two theorems are proved: one of them concerns on the passivity of linear fractional inductors and capacitors, and the other states the passivity of fractional mutual inductors; then based on above 2 theorems, the main passivity criteria stated by other 2 theorems are proposed, and a float-chart and some examples are given for demonstration of the passivity judgment.…”

Section: Figurementioning

confidence: 99%

Multivariate theory‐based passivity criteria for linear fractional networks

Liang

2018

Circuit Theory & Apps

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Summary In traditional linear network theory, the positive‐real (PR) criteria are widely used to judge the passivity of elements and networks in the light of the fact that there exists an equivalent relationship between the passivity and the PR property of their immittance functions (matrices). However, the equivalence will no longer hold when the fractional elements are introduced into the network, and the PR criteria are not suitable in complex frequency domain anymore. On the other hand, the rapid development of fractional‐order circuits and systems and the corresponding study in fractional circuit analysis and designs put forward an urgent requirement for the passivity criterion, which can tackle linear fractional networks. Hence, in this paper, we propose new passivity criteria for linear fractional networks by aid of generalized Tellegen's theorem and multivariable PR theory. By using the proposed criteria, the passivity of linear fractional networks can be judged, and the steps of the proposed criterion are illustrated by examples.

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Synthesis of two-dimensional losslessm-Ports with prescribed scattering matrix

Cited by 67 publications

References 14 publications

Transformation approach to numerically integrating PDEs by means of WDF principles

Transformation approach to numerically integrating PDEs by means of WDF principles

Scattering Systems with Several Evolutions and Formal Reproducing Kernel Hilbert Spaces

Multivariate theory‐based passivity criteria for linear fractional networks

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