Abstract
This paper discusses the behavior of the second-order modes (Hankel singular values) of linear discrete-time systems under bounded-real transformations, where the transformations are given by arbitrary transfer functions with magnitude bounded by unity. Our main result reveals that the values of the second-order modes are decreased under any of the above-mentioned transformations. This result is the generalization of the theory of Mullis and Roberts, who proved that the second-order modes are invariant under any allpass transformation, i.e. any lossless boundedreal transformation. We derive our main result by describing the controllability/observability Gramians of transformed systems with the help of the discrete-time bounded-real lemma.
| Original language | English |
|---|---|
| Pages (from-to) | 2510-2515 |
| Number of pages | 6 |
| Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
| Volume | E90-A |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 2007 Nov |
Keywords
- Bounded-real transformation
- Controllability gramian
- Discrete-time bounded-real lemma
- Discrete-time state-space system
- 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