Analysis of second-order modes of linear continuous-time systems under positive-real transformations

Shunsuke Koshita; Yousuke Mizukamit; Taketo Konno; Masahide Abe; Masayuki Kawamata

Analysis of second-order modes of linear continuous-time systems under positive-real transformations

Shunsuke Koshita, Yousuke Mizukamit, Taketo Konno, Masahide Abe, Masayuki Kawamata

ENG - Electronic Engineering

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

2 Citations (Scopus)

Abstract

This paper discusses the behavior of the second-order modes of linear continuous-time systems under variable transformations with positive-real functions. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.

Original language	English
Article number	4253121
Pages (from-to)	2248-2251
Number of pages	4
Journal	Proceedings - IEEE International Symposium on Circuits and Systems
Publication status	Published - 2007 Sep 27
Event	2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007 - New Orleans, LA, United States Duration: 2007 May 27 → 2007 May 30

ASJC Scopus subject areas

Electrical and Electronic Engineering

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title = "Analysis of second-order modes of linear continuous-time systems under positive-real transformations",

abstract = "This paper discusses the behavior of the second-order modes of linear continuous-time systems under variable transformations with positive-real functions. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.",

author = "Shunsuke Koshita and Yousuke Mizukamit and Taketo Konno and Masahide Abe and Masayuki Kawamata",

year = "2007",

month = sep,

day = "27",

language = "English",

pages = "2248--2251",

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

issn = "0271-4310",

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note = "2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007 ; Conference date: 27-05-2007 Through 30-05-2007",

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TY - JOUR

T1 - Analysis of second-order modes of linear continuous-time systems under positive-real transformations

AU - Koshita, Shunsuke

AU - Mizukamit, Yousuke

AU - Konno, Taketo

AU - Abe, Masahide

AU - Kawamata, Masayuki

PY - 2007/9/27

Y1 - 2007/9/27

N2 - This paper discusses the behavior of the second-order modes of linear continuous-time systems under variable transformations with positive-real functions. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.

AB - This paper discusses the behavior of the second-order modes of linear continuous-time systems under variable transformations with positive-real functions. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.

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M3 - Conference article

AN - SCOPUS:34548834476

SP - 2248

EP - 2251

JO - Proceedings - IEEE International Symposium on Circuits and Systems

JF - Proceedings - IEEE International Symposium on Circuits and Systems

SN - 0271-4310

M1 - 4253121

T2 - 2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007

Y2 - 27 May 2007 through 30 May 2007

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