TY - JOUR
T1 - Analysis of second-order modes of linear continuous-time systems under positive-real transformations
AU - Koshita, Shunsuke
AU - Mizukami, Yousuke
AU - Konno, Taketo
AU - Abe, Masahide
AU - Kawamata, Masayuki
PY - 2008
Y1 - 2008
N2 - This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under variable transformations with positive-real functions. That is, given a transfer function H(s) and its second-order modes, we analyze the second-order modes of transformed systems H(F(s)), where 1/F(s) is an arbitrary positive-real function. 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 (Hankel singular values) of linear continuous-time systems under variable transformations with positive-real functions. That is, given a transfer function H(s) and its second-order modes, we analyze the second-order modes of transformed systems H(F(s)), where 1/F(s) is an arbitrary positive-real function. 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.
KW - Controllability gramian
KW - General positive-real transformation
KW - Linear continuous-time system
KW - Lossless positive-real transformation
KW - Observability Gramian
KW - Second-order mode (Hankel singular value)
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U2 - 10.1093/ietfec/e91-a.2.575
DO - 10.1093/ietfec/e91-a.2.575
M3 - Article
AN - SCOPUS:77951149018
VL - E91-A
SP - 575
EP - 583
JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
SN - 0916-8508
IS - 2
ER -