Spectral factorization using the delta operator

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In recent years many papers have been published abouth the gamma-operator, mostly caused by the better numerical properties and the rapprochement between continuous and discrete time. A major problem within the LQG-design of a delta-based input-output relation has been how to spectral-factorize in an efficient way. The discrete-time method of Kuccera will not be applied since numerical word-length characteristics will be poor for fast sampling rates. In this paper a new approach is considered. A new gamma-operator (Tustin operator) is introduced, in order to make an iterative and numerical stable solution to the spectral factorization problem. The key idea is to use the gamma-operator resembled by its behavior to the differential operator.
Original languageEnglish
JournalSystems and Control Letters
Issue number5
Pages (from-to)293-301
Publication statusPublished - 1994


  • δ-operator
  • Tustin operator
  • Spectral factorization
  • LQD design
  • Adaptive control


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