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.
|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