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

Peter H. Bauer; Kamal Premaratne

doi:10.1109/81.586026

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 journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Pages (from-to)	529-537
Number of pages	9
Journal	IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume	44
Issue number	6
DOIs	https://doi.org/10.1109/81.586026
State	Published - 1997
Externally published	Yes

Keywords

Delta operator
Fixed point arithmetic
Limit cycles
Quantization error

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/81.586026

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

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.",

keywords = "Delta operator, Fixed point arithmetic, Limit cycles, Quantization error",

author = "Bauer, {Peter H.} and Kamal Premaratne",

note = "Funding Information: Manuscript received February 6, 1995; revised November 5, 1995. This work was supported by two Grants from the Office of Naval Research (ONR): N 00014-94-1-0454 and N 00014-94-1-0387. This paper was recommended by Associate Editor I. Pitas. P. H. Bauer is wtih the Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556 USA. K. Premaratne is with the Department of Electrical and Computer Engineering, University of Miami, Coral Gables, FL 33124 USA. Publisher Item Identifier S 1057-7122(97)03517-4.",

year = "1997",

doi = "10.1109/81.586026",

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T1 - Limit cycles in delta-operator formulated 1-d and m-d discrete-time systems with fixed-point arithmetic

AU - Bauer, Peter H.

AU - Premaratne, Kamal

N1 - Funding Information: Manuscript received February 6, 1995; revised November 5, 1995. This work was supported by two Grants from the Office of Naval Research (ONR): N 00014-94-1-0454 and N 00014-94-1-0387. This paper was recommended by Associate Editor I. Pitas. P. H. Bauer is wtih the Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556 USA. K. Premaratne is with the Department of Electrical and Computer Engineering, University of Miami, Coral Gables, FL 33124 USA. Publisher Item Identifier S 1057-7122(97)03517-4.

PY - 1997

Y1 - 1997

N2 - 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.

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.

KW - Delta operator

KW - Fixed point arithmetic

KW - Limit cycles

KW - Quantization error

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

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