A supplement to the Brune synthesis

Reza, F.M.

doi:10.1109/tce.1955.6372249

Cited by 16 publications

(4 citation statements)

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“…a biquadratic function that is minimum. (This result was also given by Reza in [32].) Seshu also proved that a transformerless realisation of any minimum function requires at least three reactive elements.…”

Section: The Electrical and Mechanical Analogysupporting

confidence: 61%

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Recent Advances in Learning and Control

Blondel¹,

Boyd²,

Kimura³

2008

Lecture Notes in Control and Information Sciences

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Section: The Electrical and Mechanical Analogysupporting

confidence: 61%

“…The concepts of passivity and dissipativity have been used for analyzing synchronization behavior in [7,9,24,25,32]. In this work we extend our earlier work on output synchronization of passive nonlinear systems [7,8,9,10] in two main directions.…”

Section: Introductionmentioning

confidence: 83%

Recent Advances in Learning and Control

Blondel¹,

Boyd²,

Kimura³

2008

Lecture Notes in Control and Information Sciences

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“…'s in the above sense is a normalized P.R.F. The inverse of the operation (3) has not yet been discussed. For simplicity consider the case of two P.R.F.…”

Section: Corollarymentioning

confidence: 99%

A Multiplication Theorem for Positive Real Functions

Reza¹

1958

Proceedings of the American Mathematical Society

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Modern network synthesis relies heavily on the use of Positive Real Functions. A function Z(s) of the complex frequency s is said to be a P.R.F. (short for Positive Real Function) when it satisfies the following three conditions. (a) Z(s) is analytic and single valued for Re s^O except possibly for poles on the imaginary axis, (b) Z(s) is real for real s, (c) Re Z(s) ^ 0 for Re 5 ^ 0. When in addition Re Z(iy)=0, the function Z(s) will be called an

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“…The apparent non-minimality of the construction has subsequently intrigued many researchers and there were a number of important papers which followed up on this question, e.g. [2], [3], [4], [5]. Interest in the topic lost momentum in the early 1970s due to the growing importance of integrated circuits.…”

Section: Introductionmentioning

confidence: 99%

Synthesis of positive-real functions with low-complexity series-parallel networks

Jiang

Smith

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-The purpose of this paper is to continue to develop the recently introduced concept of a regular positivereal function and its application to the classification of lowcomplexity two-terminal networks. This paper studies five-and six-element series-parallel networks with three reactive elements and presents a complete characterisation and graphical representation of the realisability conditions for these networks. The results are motivated by an approach to passive mechanical control which makes use of the inerter device.

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A supplement to the Brune synthesis

Cited by 16 publications

References 0 publications

Recent Advances in Learning and Control

Recent Advances in Learning and Control

A Multiplication Theorem for Positive Real Functions

Synthesis of positive-real functions with low-complexity series-parallel networks

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