Abstract
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, lowpasshighpass, 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.
| Original language | English |
|---|---|
| Pages (from-to) | 1481-1486 |
| Number of pages | 6 |
| Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
| Volume | E90-A |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 2007 Jul |
| Externally published | Yes |
Keywords
- Continuous-time state-space system
- Controllability Gramian
- Frequency transformation
- Invariance
- 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