Gramian-Preserving Frequency Transformation for Linear Discrete-Time State-Space Systems

Shunsuke KOSHITA  Satoru TANAKA  Masahide ABE  Masayuki KAWAMATA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.10   pp.3014-3021
Publication Date: 2008/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.10.3014
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Systems and Control
Keyword: 
discrete-time state-space system,  frequency transformation,  controllability Gramian,  observability Gramian,  allpass function,  normalized lattice structure,  

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Summary: 
This paper proposes the Gramian-preserving frequency transformation for linear discrete-time state-space systems. In this frequency transformation, we replace each delay element of a discrete-time system with an allpass system that has a balanced realization. This approach can generate transformed systems that have the same controllability/observability Gramians as those of the original system. From this result, we show that the Gramian-preserving frequency transformation gives us transformed systems with different magnitude characteristics, but with the same structural property with respect to the Gramians as that of the original system. This paper also presents a simple method for realization of the Gramian-preserving frequency transformation. This method makes use of the cascaded normalized lattice structure of allpass systems.