NDLI: Stability of Shift-Varying 2-D State-Space Digital Filters

Content Provider	IEEE Xplore Digital Library
Author	Mabey, G.W. Bose, T. Mei-Qin Chen
Copyright Year	2004
Abstract	Stability conditions for 2-D shift-varying systems are presented. The shift-varying nature of such systems emerges in applications such as adaptive filtering or adaptive image processing, where the coefficients are neither static nor periodic. The forms considered in this paper are the Givone-Roesser and the Fornasini-Marchesini models, both of which are discrete 2-D state-space filters. The sufficient conditions for BIBO stability that are proven herein are an outgrowth of the 1-D time-varying state-space conditions that have been previously established. The nature of feedback in the 2-D space is explored and found to be much more complex than for the 1-D case. However, it is also shown that when every feedback path is guaranteed to satisfy a variation on exponential stability, then BIBO stability of these two models can be assured. Further conditions are also established which engage the Lyapunov equation and guarantee the exponential stability requirement.
Sponsorship	IEEE Circuits and Systems Society
Starting Page	1431
Ending Page	1444
Page Count	14
File Size	4413657
File Format	PDF
ISSN	15498328
Volume Number	59
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stability criteria Circuit stability Thermal stability Equations Asymptotic stability Vectors 2-D stability Adaptive filtering Fornasini-Marchesini Givone-Roesser multidimensional filtering state-space systems
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Hardware and Architecture

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