A novel property of the second-order modes of discrete-time systems under variable transformation

Abstract— 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.

• Type: Conference
• Year: 2005
• Where: ISCAS
• Authors: Shunsuke Koshita, Masahide Abe, Masayuki Kawamata
• Keywords: Discrete-time Systems, ISCAS 2005, Second-order Modes, Variable Transformation