A novel property of the second-order modes of discrete-time systems under variable transformation

Shunsuke Koshita; Masahide Abe; Masayuki Kawamat

doi:10.1109/ISCAS.2005.1464752

A novel property of the second-order modes of discrete-time systems under variable transformation

Shunsuke Koshita, Masahide Abe, Masayuki Kawamat

ENG - Electronic Engineering

Research output: Contribution to journal › Conference article › peer-review

2 Citations (Scopus)

Abstract

This paper derives a novel property of the secondorder modes of discrete-time systems under variable transformation. This is the generalization of the theory presented by Mullis and Roberts, who discovered the invariance of the second-order modes under allpass transformation (variable transformation of lossless bounded-real function) and the relationship of this invariance to the roundoff noise of digital filters. This paper proves that the values of the second-order modes are decreased under any variable transformation of bounded-real function. The proof is achieved with the help of the bounded-real lemma and formulation of the controllability and observability Gramians of transformed discrete-time systems.

Original language	English
Article number	1464752
Pages (from-to)	972-975
Number of pages	4
Journal	Proceedings - IEEE International Symposium on Circuits and Systems
DOIs	https://doi.org/10.1109/ISCAS.2005.1464752
Publication status	Published - 2005
Event	IEEE International Symposium on Circuits and Systems 2005, ISCAS 2005 - Kobe, Japan Duration: 2005 May 23 → 2005 May 26

ASJC Scopus subject areas

Electrical and Electronic Engineering

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title = "A novel property of the second-order modes of discrete-time systems under variable transformation",

abstract = "This paper derives a novel property of the secondorder modes of discrete-time systems under variable transformation. This is the generalization of the theory presented by Mullis and Roberts, who discovered the invariance of the second-order modes under allpass transformation (variable transformation of lossless bounded-real function) and the relationship of this invariance to the roundoff noise of digital filters. This paper proves that the values of the second-order modes are decreased under any variable transformation of bounded-real function. The proof is achieved with the help of the bounded-real lemma and formulation of the controllability and observability Gramians of transformed discrete-time systems.",

author = "Shunsuke Koshita and Masahide Abe and Masayuki Kawamat",

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journal = "Proceedings - IEEE International Symposium on Circuits and Systems",

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AU - Koshita, Shunsuke

AU - Abe, Masahide

AU - Kawamat, Masayuki

PY - 2005

Y1 - 2005

N2 - This paper derives a novel property of the secondorder modes of discrete-time systems under variable transformation. This is the generalization of the theory presented by Mullis and Roberts, who discovered the invariance of the second-order modes under allpass transformation (variable transformation of lossless bounded-real function) and the relationship of this invariance to the roundoff noise of digital filters. This paper proves that the values of the second-order modes are decreased under any variable transformation of bounded-real function. The proof is achieved with the help of the bounded-real lemma and formulation of the controllability and observability Gramians of transformed discrete-time systems.

AB - This paper derives a novel property of the secondorder modes of discrete-time systems under variable transformation. This is the generalization of the theory presented by Mullis and Roberts, who discovered the invariance of the second-order modes under allpass transformation (variable transformation of lossless bounded-real function) and the relationship of this invariance to the roundoff noise of digital filters. This paper proves that the values of the second-order modes are decreased under any variable transformation of bounded-real function. The proof is achieved with the help of the bounded-real lemma and formulation of the controllability and observability Gramians of transformed discrete-time systems.

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JO - Proceedings - IEEE International Symposium on Circuits and Systems

JF - Proceedings - IEEE International Symposium on Circuits and Systems

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T2 - IEEE International Symposium on Circuits and Systems 2005, ISCAS 2005

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