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# Stability of weighted darma filters

Published:1998-03-01
Printed: Mar 1998
• K. J. Harrison
• J. A. Ward
• L-J. Eaton
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## Abstract

We study the stability of linear filters associated with certain types of linear difference equations with variable coefficients. We show that stability is determined by the locations of the poles of a rational transfer function relative to the spectrum of an associated weighted shift operator. The known theory for filters associated with constant-coefficient difference equations is a special case.
 Keywords: Difference equations, adaptive $\DARMA$ filters, weighted shifts, stability and boundedness, automatic continuity
 MSC Classifications: 47A62 - Equations involving linear operators, with operator unknowns 47B37 - Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 93D25 - Input-output approaches 42A85 - Convolution, factorization 47N70 - Applications in systems theory, circuits, and control theory