Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 575-583 |
| Number of pages | 9 |
| Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
| Volume | E91-A |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2008 Jan 1 |
Keywords
- Controllability gramian
- General positive-real transformation
- Linear continuous-time system
- Lossless positive-real transformation
- Observability Gramian
- Second-order mode (Hankel singular value)
ASJC Scopus subject areas
- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics