Geodesic
Stability of Weighted Darma Filters
Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 49-64

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DOI

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.
DOI : 10.4153/CMB-1998-009-1
Mots-clés : 47A62, 47B37, 93D25, 42A85, 47N70, Difference equations, adaptive DARMA filters, weighted shifts, stability and boundedness, automatic continuity 
Harrison, K. J.; Ward, J. A.; Eaton, L-J. Stability of Weighted Darma Filters. Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 49-64. doi: 10.4153/CMB-1998-009-1
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     title = {Stability of {Weighted} {Darma} {Filters}},
     journal = {Canadian mathematical bulletin},
     pages = {49--64},
     year = {1998},
     volume = {41},
     number = {1},
     doi = {10.4153/CMB-1998-009-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-009-1/}
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