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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 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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