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Invariance of Second-Order Modes of Linear Continuous-Time Systems under Typical Frequency Transformations
Masayuki KAWAMATA Yousuke MIZUKAMI Shunsuke KOSHITA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2007/07/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Systems and Control
continuous-time state-space system, second-order mode (Hankel singular value), frequency transformation, invariance, controllability Gramian, observability Gramian,
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This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under typical frequency transformations, such as lowpass-lowpass, lowpass-highpass, lowpass-bandpass, and lowpass-bandstop transformations. Our main result establishes the fact that the second-order modes are invariant under any of these typical frequency transformations. This means that any transformed system that is generated from a prototype system has the same second-order modes as those of the prototype system. We achieve the derivation of this result by describing the state-space equations and the controllability/observability Gramians of transformed systems.