Stability of shift-varying 2-D state-space digital filters

Glen W. Mabey, Tamal Bose, Mei Qin Chen

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Article number6166911
Pages (from-to)1431-1444
Number of pages14
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number7
StatePublished - 2012


  • 2-D stability
  • Adaptive filtering
  • Fornasini-Marchesini
  • Givone-Roesser
  • multidimensional filtering
  • state-space systems

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Hardware and Architecture


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