Limit cycles in delta-operator formulated 1-d and m-d discrete-time systems with fixed-point arithmetic

Peter H. Bauer, Kamal Premaratne

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, the problem of global asymptotic stability of δ-operator formulated one-dimensional (1-D) and multidimensional (m-D) discrete-time systems is analyzed for the case of fixed point implementations. It is shown that the free response of such a system tends to produce improper equilibrium points if conventional quantization arithmetic schemes such as truncation or rounding are used. Explicit necessary conditions for global asymptotic stability are derived in terms of the sampling period. These conditions demonstrate that, in many cases, fixed-point arithmetic does not allow for global asymptotic stability in δ-operator formulated discrete-time systems that use a short sampling period. This is true for the 1-D as well as the m-D case.

Original languageEnglish
Pages (from-to)529-537
Number of pages9
JournalIEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume44
Issue number6
DOIs
StatePublished - Dec 1 1997
Externally publishedYes

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Fixed point arithmetic
Asymptotic stability
Sampling

Keywords

  • Delta operator
  • Fixed point arithmetic
  • Limit cycles
  • Quantization error

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

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AB - In this paper, the problem of global asymptotic stability of δ-operator formulated one-dimensional (1-D) and multidimensional (m-D) discrete-time systems is analyzed for the case of fixed point implementations. It is shown that the free response of such a system tends to produce improper equilibrium points if conventional quantization arithmetic schemes such as truncation or rounding are used. Explicit necessary conditions for global asymptotic stability are derived in terms of the sampling period. These conditions demonstrate that, in many cases, fixed-point arithmetic does not allow for global asymptotic stability in δ-operator formulated discrete-time systems that use a short sampling period. This is true for the 1-D as well as the m-D case.

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