This paper derives a novel property of the secondorder modes of discrete-time systems under variable transformation. This is the generalization of the theory presented by Mullis and Roberts, who discovered the invariance of the second-order modes under allpass transformation (variable transformation of lossless bounded-real function) and the relationship of this invariance to the roundoff noise of digital filters. This paper proves that the values of the second-order modes are decreased under any variable transformation of bounded-real function. The proof is achieved with the help of the bounded-real lemma and formulation of the controllability and observability Gramians of transformed discrete-time systems.
|Number of pages||4|
|Journal||Proceedings - IEEE International Symposium on Circuits and Systems|
|Publication status||Published - 2005|
|Event||IEEE International Symposium on Circuits and Systems 2005, ISCAS 2005 - Kobe, Japan|
Duration: 2005 May 23 → 2005 May 26
ASJC Scopus subject areas
- Electrical and Electronic Engineering