Canad. Math. Bull. 41(1998), 49-64
Printed: Mar 1998
K. J. Harrison
J. A. Ward
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.
Difference equations, adaptive $\DARMA$ filters, weighted shifts, stability and boundedness, automatic continuity
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