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 Difference equations, adaptive $\DARMA$ filters, weighted shifts, stability and boundedness, automatic continuity

MSC Classifications:

47A62, 47B37, 93D25, 42A85, 47N70 show english descriptions Equations involving linear operators, with operator unknowns
Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Input-output approaches
Convolution, factorization
Applications in systems theory, circuits, and control theory 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

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