Analysis of Second-Order Modes of Linear Continuous-Time Systems under Positive-Real Transformations

Abstract— This paper discusses the behavior of the secondorder 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 positivereal lemma, and state-space formulation of transformed systems.

• Type: Conference
• Year: 2007
• Where: ISCAS
• Authors: Shunsuke Koshita, Yousuke Mizukami, Taketo Konno, Masahide Abe, Masayuki Kawamata
• Keywords: General Positive-real Transformation, ISCAS 2007, Lossless Positive-real Transformation, Positive-real Transformation